My brother's the pianist and the one getting a music degree, so I'm going to let him write this post:
Hey,
I'm a music theory major and piano principle at college, so I might be able to help. I have been playing for 11 years though, so some of the stuff I do is just so natural that it is hard for me to explain it. . . but hey, I'll give it a try

Anyway, the first thing to remember is that it does take LOTS of patience, some people have more skill at memorizing than others but if you are willing to put enough time into it you can memorize almost anything. The next important thing is to realize that what you are actually doing is creating "muscle memory" that is to say, you aren't actually going to be consciously thinking about every note, or remembering the page of music and reading it in your mind (I've had some friends of mine try and do that, it was funny), what is actually happening is more like developing reflexes. It becomes almost automatic, so that when you start playing your hands just know where to go. Now, I say "almost" automatic because you still have to be consciously aware of the piece enough to fix any mistakes that might happen during performance, but don't worry too much. I think this balance between the automatic and the conscious is something that just kind of naturally happens.
Now, about the actual process of memorizing. The key is SMALL chunks! When I am trying to memorize a piece I take a small section (anywhere from a line to just two measures, depending on how complicated it is) and play it as best as I can with the the music first (about 5 to 10 times) then I start to work without the music, again in small chunks, and as slow as I need to go to make it perfect (remember, you can always learn to speed it up later, it is more important to learn it correctly first). Once I can do this small section without music perfectly 15 times (that means NO mistakes) I stop and take a break . . . anymore than this gets really boring really quickly, at least for me, I have some friends that spend more time on a section, but hey. . . Now, as you start to memorize more and more bits of the music you can begin to string them together. Once again this takes time, but if you have memorized it in chucks it is like working with pieces of a puzzle that you already know, instead of doing the whole thing from scratch. Oh, and I don't know if this would help you, but some people learn each hand separately and then put them together. I've never had much luck with that method, but it is a good way to make sure that you know both parts backward and forward. I guess the bottom line is don't just try and play the whole piece over and over again in order to memorize it. I used to do that, and while you will learn it eventually, it is a really ineffective method. Smaller sections really are the key. I know it is tedious, but if you have patience and take it slow in the end it really pays off! Anyway, I hope this was helpful, it was all kind of off the top of my head so, I don't know if it makes much sense. But either way, good luck and I hope your music learning goes well!
