God, I used to love assignments like that.
I can still readily recall Portia's speech from "The Merchant of Venice" that we had to memorize when I was in 7th grade!
I was always good at remembering stuff like that; I used to have to remember whole speeches for oratorical contests when I was younger--2 and 3 typed pages of speech, no note cards, no teleprompters...
Just read and recite. Read and recite. As a parent, you can help him a great deal. My mom wrote my speeches and she'd go over them with me repeatedly--while I ate, while I watched TV, etc. The bad thing is that I did all that stuff maybe 20 or so years ago, so I don't remember many of my techniques. I think I did do as suggested above, though, and start with one sentence (line), commit that to memory, add another line, commit both to memory, so on and so forth.
One thing I didn't do, though, when having to memorize Shakespeare or Chaucer or something, was try to translate it into modern English. I was the type of learner who would have just been more confused by that, so I just stuck with what was in the textbook.