Answer: As for memorizing the Qur’aan, then the people differ, from the people there are those that are able to memorize a page, and from them there are those that can memorize both sides of a page; and from them there are those that are not able to memorize except half a page or less (than that), so everyone according to their ability.
From the affairs that which aid in memorizing the Qur’aan are repetition, revision and standing in the night prayer with it (i.e. that which you have memorized) if you are able to perform the night prayer. For indeed Allaah, the One free from all imperfections and the Most High says:
Verily, the rising by night (for Tahajjud prayer) is very hard and most potent and good for governing (the soul), and most suitable for (understanding) the Word (of Allâh). [Soorah Al-Muzzammil 73:6]
And in some parts of the night (also) offer the Salât (prayer) with it (i.e. recite the Qur’an in the prayer), as an additional prayer (Tahajjud optional prayer Nawâfil) for you (O Muhammad sallAllaahu ‘alayhi wa sallam). [Soorah Al-Isra 17:79]
Likewise taking from the Mashaykh and memorizing at their hands. If you do not find them, then I advise you to stick to the cassettes of the proficient reciters, those whom recite with a sound recitation, and not those who exaggerate as ‘Abdul Baasit does; rather, the recitation of just balanced sound reciters and not those that (recite in a manner) that was disliked by some of the Salaf.
As for the memorization of Hadeeth, then they are little easier if it is done without the Asaaneed (chains of narration), so it is possible that you memorize a Hadeeth in a day or two days or three days then act upon this hadeeth, for indeed this aids in making the Hadeeth firmly grounded, then studying with the brothers and lots of repetition.
[Shaykh Muqbil bin Haadee|Tuhfatul Mujeeb ‘Alaa Asilatil-Hadhir wal-Ghareeb, p.157, Dar al-Aathar|Translated by Abu Maryam Taariq bin ‘Ali]