Allah has made the Quran easy to read, understand and memorize for those who sincerely want to embrace the divine words. He repeated four times in the Quran, in chapter Al Qamar:
And We have certainly made the Qur’an easy for remembrance, so is there any who will remember? (54:17)
The above verse holds true all the time, even if our first language is not Arabic. Allah Himself has promised us, You just need to try, He will make it easy.
The fact that millions of Muslims all over the world, from multitudes of nationalities and languages, know at least some part of the Quran by heart, is nothing but a manifestation of the above mentioned verse.
The same cannot be said for any other book in world history. If you were ever forced to memorize your school work by heart, you know what I am talking about.
So, it doesn’t matter whether you don’t know a word of the Quran, or whether you know some chapters by heart; no matter what your level, you will find Quran memorization easy, all you need to do is sincerely try for the sake of Allah.
Prerequisites
Some people have this notion that you need to have near-perfect tajweed (i.e. correct recitation) in order to recite Quran. That is not at all true. Allah has not ordered us to recite perfectly. He just said “recite”! Allah has said:
Fear Allah as much as you can. (64:16)
It doesn’t matter whether you can tell the difference between a qaaf and a kaaf, just give it a start! And as you keep reciting and memorizing, learn proper recitation along the way.
Selecting the Easiest Surahs to Memorize
Now when it comes to selecting chapters to memorize, the general rule is that the easiest ones are from the last chapters backwards.
Juz Amma (the last 1/30th of the Quran) contains Makki chapters, which have short verses that often rhyme, and are overall shorter than the Madini chapters.
The last ten chapters (105 to 114), Surat al Asr (103)and Surat al Qadr (97) are particularly short and easy to memorize. Nonetheless, you don’t really need to follow any sequence in memorizing chapters, neither do you need to memorize whole chapters, although it is better to go about it in a systematic way.
You can pick up ayah from anywhere in the Quran, memorize them and recite them in your prayers, as long as their total length is equivalent to three short verses.
Some Final Words: Understanding What You Recite
In order to find maximum benefit from the chapters that you memorize and recite during prayers, you should have at least some knowledge of what you are reciting.
When it comes to being aware of the meaning of the words you are reciting in prayer, I personally have found the mere reading of translations very inadequate.
Here are some better ways:
Listen to some lectures on tafsir (explanation) of the chapter that you are memorizing, or read the chapter from Tafsir ibn Kathir, which is available free online in English translation.
This way you will know in depth the meaning of the verses, the contexts of their revelation and the stories behind them. The more knowledge you associate with the verses, the easier you will find to memorize them and absorb their meanings.
Memorize at least some of the vocabulary of the verses. You will find a free Quran word by word translation here.
Just note down some of the words and memorize their meanings. This way you will be aware of what you are saying when you say those words during recitation.
Source: Understand Quran.