السلام عليكم ورحمة الله
I have been teaching the Quranic lessons ( Tajweed ) to foreigns. Well, I don't know your level in Arabic, it supports to be an intermediate level.
I personnaly advice you to make a serious plan for reading Quran and using the explaining of AYAAT in Quran. The method is:
1- Reading 10 AYAAT by Day, everytime you're free. (Just reading) [prefering with Tajweed]
2- When you got the correct pronounciation, then try to read sentence by sentence with explaining why it says that, and understanding the meaning in the sentences, and some specific words*.
3 - After all of that, you memorize the 10 sentences* by heart.
4- You go to the second 10 sentences and do the same first step (1) by starting from the last sentences you have memorized.
5- Trying to explain the sentences again (using books).
6 - Memorizing the sentences.
I am sure if you take the method seriously, you'll be able to understand and memorizing the Quran as well as an Arabic speaker. Also, it is going to help improving your skills in Arabic.
* It is recommended to understand the full meaning. Then, asking about the specific words.
For more questions, feel free to ask.
السلام عليكم