Below is a transcription of a lecture on how to benefit from the blessed days of Dhul-Hijjah by Umm ‘Abdur-Rahman. May Allah reward the sister who transcribed the lecture.
“By the ten nights.” [Al-Fajr 89:2]
The “ten nights” which Allah [subhana wa ta’ala] is swearing by here, are the first 10 days of Dhul-Hijjah.  Allah [subhana wa ta’ala] swears an oath by them, and swearing an oath by something is indicative of its importance and great benefit.
Ibn ‘Abbas [radi Allahu ‘anhu] narrated that Prophet [sall-Allahu ‘alayhi wa sallam] said: “There is no deed more precious in the sight of Allah, or greater in reward, than a good deed done during the ten days of Sacrifice.” He was asked: “Not even jihad for the sake of Allah?” He said: “Not even jihad for the sake of Allah, except in the case of a man who went out to fight giving himself and his wealth up for the cause, and came back with nothing.” 
So, my sisters take note of the following:
Have the intention to spread this important information.
It is a great chance to collect uncountable hasanat . It is a great chance to renew your relation with Allah [subhana wa ta’ala]. Prepare now so you can start from the first night/day of the month [i.e. as soon as Dhul-Hijjah is announced]. You don’t want to miss a moment of the best days in the sight of Allah [subhana wa ta’ala].
Since the Prophet [sall-Allahu ‘alayhi wa sallam] referred to the 10 days of Dhul-Hijjah as: “…no days better than these days in the sight of Allah.” , the scholars have said that these are better than Ramadan.  Therefore, be very vigilant and don’t waste these precious moments. Ask Allah to help you to benefit from this period of His special Grace.
Ask yourself these questions [non-rhetorical]:
Did you intend to benefit from these days?
What have you done to prepare for these 10 days?
Did you prepare a program?
What is your plan of action?
Here is a brief guide to help you to prepare for the best days of the year :
Read the Qur’an:
Plan to complete the reading of the Qur’an within this period.
If you read three juz a day, it can be accomplished. It is not difficult. Ask Allah to make it easy for you. We know reciting one letter is equal to ten hasanat . If you read three juz everyday, it translates to thousands of millions of hasanat.
Subhana’Allah! And this calculation is just based on the 1=10 ratio. These are special days of His Grace. Therefore, don’t even think about how much Allah can/will increase & add it for you. You cannot fathom it. He is Kareem. He knows that you have ikhlas ; He will not count it as 1=10. He could raise it to 1=700 or even more. And this is what you can earn every day of these special days. Keep in mind that reciting the Qur’an is a good deed and Allah specially loves the good deeds done in these days: “And if He [subhana wa ta’ala] loves the good deeds, He will love the doer of those good deeds.”  If Allah loves someone, He will not punish them. Remember this concept so that the deeds you do come from your heart [don’t be like a machine]. Honour the rights of the Qur’an when reciting it.
Increase in Nawafil Prayers:
Increase your supererogatory prayers.
Ask yourself these questions and make sure that your heart gives you sincere answers:
Do you have an aim?
Do you really want to be closer to Allah?
Do you live with this craving?
Do you really love Allah and seek His closeness?
If, you want this, then know that Allah teaches you the means to gaining His qurb .
“Fall prostrate and draw near to Allah!” [Al-Alaq 96:19]
This is the way! Prostrate in sujud to Him [subhana wa ta’ala] and you will be closer to Him. The Prophet [sall-Allahu ‘alayhi wa sallam] said: “The closest that a person is to his Lord is when he is prostrating, so say a great deal of du’a then.”  He [sall-Allahu ‘alayhi wa sallam] is commanding us to make a lot of du’a while in sujud. Are we obeying his order? Yes? We need to do more. For he [sall-Allahu ‘alayhi wa sallam] said to: “…make lots of du’a.” Remember, the Prophet [sall-Allahu ‘alayhi wa sallam] loved us and he knew that we have a lot of needs from Allah. This is why he taught us the way to get those needs fulfilled. Therefore, if you have needs, then you cannot leave sujud. Any sajdah without khushu’ & without du’a is a big khasara . Let us not be losers from now on bi-idhnillah.
When the Prophet [sall-Allahu ‘alayhi wa sallam] instructed us to do a lot of sujud, it means to perform a lot of salah . “With each sajdah for Allah, He will raise you a level with it. And cancel a sin with it.” So, the more you increase in your sujud, the closer you are to being a winner.
Examples for increasing nawafil salah :
a] Salat Dhuha: Also known as al-Awwabeen, may be offered as 2, 4, 6 or 8 rak’at, prayed after the sun has risen and before the time for Dhuhr approaches.  “Al-Awwab’ means one who is obedient, or one who turns to obedience. Bi-idhnillah, we want to show Allah that we are of those who are obedient.
b] 4 rak’at before and 4 after Dhuhr: “Whoever regularly performs four rak’at before Dhuhr and four after it, Allah will forbid him to the Fire.” 
c] 4 rak’at before ‘Asr – The Prophet [sall-Allahu ‘alayhi wa sallam] said: “May Allah have mercy on those who pray four rak’at before ‘Asr prayer.”  Bi-idhnillah, you stand to gain the mercy of Allah because of the du’a of Prophet [sall-Allahu ‘alayhi wa sallam]. Do you want the mercy of Allah to reach you? Don’t leave these 4 rak’at.
d] Tahhiyatul masjid: Greet the masjid with two rak’at: “If any one of you enters a mosque, he should pray two rak’at before sitting.” 
e] Salat at-Tawbah: It could be any bad deed, any sin, you hear something bad , you see something bad, you feel your heart constricted because of something you have done and you didn’t mean it, etc, you can erase it immediately with your prayer of repentance. Make a good wudhu’ and offer two sincere rak’at of repentance. Ask Allah to forgive you. If it’s from your heart, then know that Allah will cancel your sin.
g] Qiyam al-Layl: With this prayer, we hope that Allah will illuminate our graves; will bestow nur on our faces; will cancel our bad deeds, bi-idhnillah. Pray at least 2 rak’at. If you are able to follow the Sunnah, then pray all 11 rak’at .
Remember that in these special days and nights, Allah is sending His special mercy. Do you think that this special mercy will reach everybody? Do you think that it will reach the one who is in front of the TV watching a movie? Or listening to music? Or do you think it will reach the one who is making sujud, ruku’, tilawah, making istighfar, etc.?
We have to show Allah that we want this special mercy. We need to make ourselves eligible for it.
Allah [subhana wa ta’ala] swears by the night . Therefore, take care of the nights. Don’t be among the losers. Write this in bold and make it your motivational factor for the special days: “We won’t be among the losers!” Remember: “Our Lord, may He be blessed and exalted, comes down to the lowest heaven every night when the last third of the night is left, and He says: ‘Who will call upon Me, that I may answer him? Who will ask of Me, that I may give him? Who will ask Me for forgiveness, that I may forgive him?’.”  And, now that it is winter, we get really long nights. So it’s a good chance to maximise our hasanat. Don’t forget while you are praying qiyam that Allah [subhana wa ta’ala] Loves this deed. Therefore, He [subhana wa ta’ala] loves the doer of this deed also.
If we were lazy before, we will be active and good from now on bi-idhnillah. We will not be among the losers. If these days and nights are a king who is distributing gifts of gold while announcing: “Come take these gold nuggets”, wAllahi, you will find people standing in long queues and hordes to collect them. Subhana’Allah, Allah is spreading mercy during these days. He [subhana wa ta’ala] is accepting supplications. He [subhana wa ta’ala] is offering unimaginably wonderful blessings that we don’t even know of. So will we not work to get in those lines to gather Allah’s gifts?
Makes lots of Dhikr:
Do a lot of dhikr, especially in these days.
“There are no days greater in the sight of Allah…” 
So what did the Prophet [sall-Allahu ‘alayhi wa sallam] tell us to do in these days? That, we need to make the dhikr of tahlil, tahmid & takbir.  As soon as the announcement of Dhul-Hijjah is made, start your dhikr:
“Allahu Akbar, Allahu Akbar, la ilaha ill-Allah, Wallahu Akbar. Walilahilhamd.”
Many people mistakenly believe that you chant this only on the day of ‘id. But, it is meant to be recited from the beginning of Dhul-Hijjah. Bukhari related that Ibn ‘Umar & Abu Hurayrah said that they used to go out in the streets making loud takbir. They did not think that this was riya . They were busy with declaring the [signs of Allah. This practice has now become a forgotten Sunnah. Why do people feel shy to follow this Sunnah? These are the days of takbir, tahlil & tahmid with raised voices.
Therefore revive this Sunnah by doing audible tasbih during all of the ten days of Dhul-Hijjah.
For women, when you are in your homes, raise your voices. You will remind your children, husbands, brothers, etc. Make it like a habit so that you will find yourself doing dhikr automatically. While walking, reclining, working, eating, just keep doing dhikr.
Send a lot of blessings and salam upon the Prophet [sall-Allahu ‘alayhi wa sallam] consistently. Just one hadith should be enough for the believer who loves Prophet [sall-Allahu ‘alayhi wa sallam]. It is enough honour that when you send your salam to Prophet [sall-Allahu ‘alayhi wa sallam], Allah returns his soul to him in order to answer you: “There is no one who sends salam upon me but Allah will restore to me my soul so that I may return his salam.”  Therefore, send your darud & salam from your heart. Feel that special honour in doing that deed.
All kinds of dhikr will make your relation with Allah stronger and stronger. How many Muslim’s are there today? 1.5 billion? In one minute it is possible to gain 1.5 billion hasanat. Allahu Akbar! How generous is Allah [subhana wa ta’ala]. No one will give you like Allah [subhana wa ta’ala] gives. So how can you gain 1.5 million hasanat? By making istighfar for all Muslim’s. The Prophet [sall-Allahu ‘alayhi wa sallam] is reported to have said that when a person seeks forgiveness for all believers, Allah will write for him a hasanat for every one of those believers.  Just say ‘Astaghfirullah’ for yourself and for all the believers, from your heart. Allah [subhana wa ta’ala] is forgiving & generous.
On the Day of Judgement, when you will see your book, you will find the record of your sins in it & you will feel regret. But, Subhana’Allah, you will find between these sins, Astaghfirullah, Astaghfirullah, Astaghfirullah. Bi-idhnillah, Allah, the Karim will cancel those sins that have istighfar beside them, around them, after them.
Luqman taught his sons to make istighfar. He said: “Oh my sons, istighfirullaha qaidun, istighfirullah qaimum, istghfirullaha raqibun [make istighfar when you are standing, sitting, reclining]. For the mercy of Allah is descending.”
Indeed, rahamat are falling down like rain. So try to be under those rahamat. Look at it this way – there are seasons of mercy during which Allah sends down abundant mercy [like during Ramadan, like the days of Dhul-Hijjah, etc.]. Allah is always generous because that is one of His [subhana wa ta’ala] Attributes, but He says that He gives more during certain periods. Allah is Rahim always, but He says He has more mercy during a certain period. These days are like those special-rate promotions or sale season. Therefore, don’t leave or ignore this sale. Go and ask for more. Keep saying ‘astaghfirullah’, ‘astaghfirullah’, astaghfirullah’, keep insisting on it till Allah forgives you. Start from the beginning of Dhul-Hijjah.
“…nor will He punish them while they seek (Allah’s) forgiveness.” [Al-Anfal 8:33]
We are informed that there is no punishment from Allah [subhana wa ta’ala a] on the yastaghfirun . Allah relieves all problems with istighfar. Those who are persistent in istighfar in their lives, disasters and calamities will be repelled from them. Mercy is like a cloud on the head of the mustaghfirin . How do we know this?
“Why seek you not the forgiveness of Allah, that you may receive mercy?” [An-Naml 27:46]
Allah is telling us to make istighfar to gain His mercy. Let your istighfar ascend to Him and His mercy will descend upon you.
Fast as much as you can during these blessed days. If you can fast all of these days, then do so. Even in any regular day, Allah has promised a great reward for the one who fasts: “Whoever fasts one day for the sake of Allah, Allah will keep his face seventy years distance away from the Fire because of it.”  So what about these special days for which it is said: “There is no deed more precious in the sight of Allah, or greater in reward, than a good deed done during the ten days of Dhul-Hijjah.” Allah loves the good deeds in these days. Allah loves siyam. Put these two beloved things together. You are the doer of the things Allah loves. He [subhana wa ta’ala] will Love you, bi-idhnillah.
Any ‘ibadah, be it salah, dhikr, Qur’an, that is done during some periods of time and with them, are also periods of non action. Can you do any of them from Fajr till Maghrib continuously? Which ‘ibadah will you be able to do non-stop? Siyam! From Fajr till Maghrib during the best days, you will be able to be in a continuous state of worship. So please my sisters [& brothers], grab this chance eagerly. Also don’t forget you have if Allah wills, at least one du’a guaranteed with each siyam – at the time of breaking the fast. So that is nine opportune moments during this period.
Regarding fasting on the day of ‘Arafah, the Prophet [sall-Allahu ‘alayhi wa sallam] said: “Fasting the day of ‘Arafah, I hope, will expiate the sins of the year before it and the year to come…”  So how does this happen? Does this mean that we can fast on that day and for the rest of the year we can do whatever we want of bad deeds? No! It implies that Allah [subhana wa ta’ala] will help us to abstain from sins. And, if you commit a sin by mistake, He [subhana wa ta’ala] will cancel it due to His promise.
Spending for the sake of Allah!
Only Allah knows how many trials & calamities have been pushed away from us, our family and loved ones as a result of our sadaqah. Allah knows how many times relief and ease has come to us due to the sadaqah we gave. Therefore, give in the way of Allah, as much as you can. Don’t leave any raised hands return empty. Show Allah that you love Him by spending from that which you love. Show Allah [subhana wa ta’ala] that all these things mean nothing besides gaining His ridha .
Don’t look and remind yourself of what you have already spent in the past. If Allah wills, He [subhana wa ta’ala] has accepted and written it for you. Now, think of how you can outdo that sadaqah during these days. Spend from what you love and Allah will love you.
Preserve the Ties of Kinship:
Preserve the ties of kinship for: “No one who severs the ties of kinship will enter Paradise.”  If it is difficult for you to call or meet every relative, then send them a message. But write with your heart and with the right intention. There is a man who connects with all of his near and far relatives. It is almost like a mission for him for the sake of Allah. He [subhana wa ta’ala] loves this ‘ibadah. Even those who are far away, he calls and connects them to the rest of the family and brings them all together. And subhana’Allaah, Allah has given him a lot of wealth and with such ease and has made his life easy, and as a result of his deeds. The Prophet [sall-Allahu ‘alayhi wa sallam] promised this reward for the one who connects and maintains kinship: “Whoever would like his rizq to be increased and his life to be extended, should uphold the ties of kinship.” 
These were just a few of the wonderful things we can do during the forthcoming best days of Dhul-Hijjah. Therefore, if we want Allah’s help with these deeds and our schedule for them, we need to do a lot of tawbah. The Salaf as-Salih used to say that they would feel prevented from qiyam al-layl due to their sins. They knew that when they want to do ‘ibadah and they are unable to do it, it is due sins. So, what do we need to do? A lot of istighfar with tawbah, real Tawbah! Ask Allah for help.
Make the du’a:
“O Allah, help me to remember You, to give You thanks, and to perform Your worship in the best manner.” 
 Ibn ‘Abbas, Ibn az-Zubayr, Mujahid and others of the earlier and later generations said that this refers to the first ten days of Dhul-Hijjah. Ibn Kathir said: “This is the correct opinion.” [Tafsir ibn Kathir, 8/413]
 Al-Bukhari, 2/457
 Ahmad, 7/224 – Ahmad Shakir stated that it is sahih
 The verses [Al-Fajr 89:1-2] and various hadith indicate that these 10 days are better than all the other days of the year, with no exceptions, not even the last ten days of Ramadan. But the last ten nights of Ramadan are better, because they include Layl al-Qadr [“the Night of Power”], which is better than a thousand months. Thus the various reports may be reconciled. [See: Tafsir ibn Kathir, 5/412]
 Shaykh Muhammad bin Salih al-‘Uthaymin
 Muslim, 482
 Muslim, 1238
 At-Tirmidhi, 428 – classed as sahih by al-Albani in Sahih al-Nasa’i
 At-Tirmidhi, 395 – classed as hasan by al-Albani in Sahih al-Jami 3493
 Al-Bukhari & Muslim
 Al-Bukhari, 1094 and Muslim, 758
 Ahmad, 7/224
 Tahlil [“La ilaha ill-Allah”], Tahmid [“Alhamdulillah”] and Takbir [“Allahu Akbar”]. See: Ahmad, 7/224
 Abu Dawud, 2041 – classed as hasan by al-Albani
 Classed as hasan by al Albani
 Muslim, 2/808
 Muslim, 1976
 Sahih Muslim
 Al-Bukhari, 5986 and Muslim, 2557
 Sahih Abu Dawud, 1/284
Allah subhanahu wa’tala says (interpretation of the meaning):
“Verily, those who say: ‘Our Lord is Allah (Alone),’ and then they stand firm, on them the angels will descend (at the time of their death) (saying): ‘Fear not, nor grieve! But receive the glad tidings of Paradise which you have been promised!'” [41:30]