I was in a Bible quiz program as a teen. For me, the best way to memorize is to repeat the first phrase of verse one to myself. Then add another phrase and quote up to the end of the phrase. Keep going until you get the whole verse. Then start on verse two, breaking it down into phrases and quoting phrases and adding new phrases until you get the whole thing. Then quote verse one and two.
Keep going until you have the whole chapter. As a teen, this process can take several hours to do the averaged-sized chapter.
Another method is to just try to memorize one verse until you can quote it, and then just go on to the next. This was my method to get a chapter 'roughed in' if I had an hour to study before a practice Bible Quiz tournament. I'd have a lot of the material in my short-term memory but i couldn't answer quotation questions. Then, when I went back and really memorized it, it was easier, becaused I had an idea of what each verse said.
Putting in several hours a week, the teens in the program could memorize a chapter a week. We did go for a few weeks for review now and then. For the year we did about 30 chapters, whether it was one book or several small epistles. We needed to have it memorized after about 7 or 8 months so we could quiz on the whole book.
The human mind has a great capability to memorize. I have read that in Jesus' day, the Judean boys on the lower rung of the educational ladder studied the first 5 books of the Torah. they memorized them, in Hebrew! This memorization probably helped them learn Hebrew if they were Aramaic speakers. They started with Leviticus, which was good for some of the same reasons we would think it's difficult. The repetition of phrases helped with memorization and the language. They learned the books over the course of 5 years.
The Bible says 'Thy word have I hid in mine heart that I might not sin against Thee...' Memorizing scripture is important.