Salamalaik,
My beloved Sheikh once told about memorizing the Qu'ran. First of all we need to purify ourselves from  sins and set our intention of memorizing it is to gain HIDAYAH. Here a few steps of memorizing Qu'ran that I quoted from http://www.alquranclasses.com/techniques-memorizing-quran/:

1.      First of all, make sure to correct your tawbah (repentance to Allah), as sins do not leave any room for the Words of Allah (swt). Imam Al-Shafie has a famous verse of poetry in which he complained to his scholar about having difficulty in memorizing and his scholar advised him to abandon sins.

In human life, memorizing is totally been influenced by our mind. In order to memorizing something logically we need calmness. Therefore, by doing tawbah we are going to bring ourself to the state on tranquility. As a result, it will lead to easiness in memorization.

2.      Have your intention ready, and bear in your mind the reward and virtues of this great deed. Rationally, by doing this we have our target what to achieve. If we want a job we will try hard by studying, hunting for it. In order to memorize the Qu’ran, the intention as objective.

3.      Dedicate a specific time each day for memorizing Quran. This method actually makes our memorization easier and more valuable. Imagine you are memorizing the Qu’ran in very busy worldly matter, how can you memorize it and if you managed to memorize it where is the rahmah in there. The Qur’an as guide, therefore we need to find it in a soothing way rather than busy way.

4.      Use the same copy of the Holy Qur’an each time. This is because your mind takes a ‘snapshot’ of the pages you use while memorizing.

5.      Start with the Surahs that are most easy for you. Many Scholars recommend beginning with the last five juz’s (the 30th, then the 29th, and so on). They suggest it due the last five juz contains short surah and ayat.

6.      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. Most of Malaysian for instance often listen to ayat-ayat lazim which started from Surah Al-Dhuha.

7. The younger you are, the easier it will be for you to memorize Qur’an. As you grow older, you get busier and thus your capacity for memorizing decreases. However, it’s never too late Insha’Allah. If you haven’t yet memorized a lot during your childhood or teens, you can still catch up.

8.      Use Audios to memorize Qur’an. It’s a proven fact that mind always catches up the audios fast and they last for longer. You may get Audio Cassettes of Qur’an recitation and can listen to it while keeping your eyes on your copy of Qur’an; this will also help you in improving your pronunciation. Alternatively, you can also read it loudly while memorizing. This will help in memorizing Qur’an fast and effectively.

9. After completing a couple of ayahs, recite them in the very next Nawafil (voluntary prayer) that you pray. Also practice them with a friend or your spouse.

10.  Finally, it might be a good idea to work in groups and 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 it best.