The companions took their time in memorisation of the quran so much so Umar Ibn Khattab took 12 years to memorise baqarah alone while in Ibn Umar took 8 year.
The scholars explain the various reasons for this, they sought to learn the fiqh, tafseer, ahkaam and reports with deep contemplation of each verse while applying this in their everyday life (10 ayah at a time) before moving on.
There is also reports that the Prophet SAWS dislike for quick memorisation of the Quran.
It's mind blowing when you reflect that this is how they studied despite the fact that the quran was in their own native tongue and was revealed in their presence.
Mindless memorisation without a deep study of tafseer or contemplation will always result in you either forgetting it quickly or making constant rookie mistakes.
I have abandoned that common ludicrous mindless path we were all taught from a young age to quickly memorise without even basic understanding when I came across these hadiths.
This is how I plan to do it it now after being exposed to those hadith's.
Grab a number of Ayah's (5-10)
1. Understand basic translation of the ayah's first - so much so you should be able to give basic English/Somali translation to someone that doesn't know.
2. Understanding basic tafseer of the ayah - When it was revealed, the circumstances of revelation and how it was understood.
3. Deep tafseer - most of it is deep linguistic-all analysis followed by in depth contemplation, especially with regards to how the ayah applies to our time and how you apply it.
4. Memorisation of those ayah's. (you will never forget them)
Pre-requisite off all this in my opinion is either listening or reading the seerah of the Prophet first.
The best material that is available in the English language is Anwar Awlaki and Yasir Qadhi, the latter is on YouTube.
The best material for points 1-3 in the English Language is Nouman Ali Khan Bayyinah podcasts (he has both basic and deep tasfeer) followed by translation of Ibn Kathir and
Tafsir Jalalayn