Abdullah ibn Amr ibn Al-As may Allah bless him reported: The Prophet peace be upon him said, "The one who was devoted to the Qur'an will be told on the Day of Resurrection: `Recite and ascend (in ranks) as you used to recite when you were in the world. Your rank will be at the last Ayah you recite.''' [Abu Dawud and At-Tirmidhi].
This Hadith mentions the merit of those who memorize part or all of the Qur'an. Some scholars, in explaining this Hadith, have mentioned that the number of ranks (levels) in Paradise is equal to the number of ayahs in the Qur’an, and that a believer will rise one rank for each ayah that he or she memorizes.
In another Hadith, Othman ibn Affan may Allah bless him reported that the Messenger of Allah peace be upon him said, "The best amongst you is the one who learns the Qur'an and teaches it.'' [Al-Bukhari].
In what follows we list a few hints regarding memorizing the Qur’an, some of which were presented to us by the knowledgeable Sh. Osama Abdul-Azeem of Al-Azhar University in Cairo, Egypt.
First, make sure to correct your tawbah (repentance to Allah), as sins do not leave any room for the Words of Allah. The Imam Al-Shafie has a famous verse of poetry in which he complained to his scholar about having difficulty in memorizing. His scholar advised him to abandon sins
Have your intention ready, and bear in mind the reward and virtues of this great deed as mentioned in the Hadiths above. Ask Allah sincerely to assist you in accomplishing this.
Dedicate a specific time each day (or every couple of days) for memorizing. This should be a time when you are not busy with other things.
Use the same copy of the Qur’an each time. This is because your mind takes a ‘snapshot’ of the pages.
Start with the surahs that are easiest to you. Many people recommend beginning with the last five juz’s (the 30th, then the 29th, and so on).
Other surahs to begin with are those that you enjoy reciting most of all, and those that you frequently listen to and thus probably already know part of by heart.
The younger you are, the easier it will be. As you grow older, you get busier and your capacity for memorizing decreases. However, it’s never too late in shaa Allah. If you haven’t memorized a lot during your childhood or teens, you can still catch up.
After completing a couple of ayahs, recite them in the next nafl (voluntary prayer) that you pray. Alternatively, practice them with a friend or your spouse.
Finally, it might be a good idea to work in groups, encouraging one another. If you are trying to get your children to memorize, you might want to create a sense of competition among them and then provide some reward to whoever memorizes best. May Allah guide us to all that pleases Him, Ameen.