Does anyone know how theater actors memorize their scripts?

Well, you have two very different issues here. In answer to your main question, there are many ways to learn lines. Constant repetition. Plenty of rehearsal. Running lines with a line partner. Typing or writing out your script. Recording your lines, and then, when your lines are starting to lock in, recording your cues (I did this last one today).

Cold line running is a biggie if you're short of time. You basically go section by section, repeating lines numerous times (five seems to be a standard), running back over them and making sure the section is down before you move on.

Stage fright is a whole other show. Confidence in your work is key. It's not something I've ever faced, so I'll refer you to these sites:

http://www.google.com.au/search?source=ig&hl=en&rl...

I just went on an audition and forgot all of my lines! It was for a tv show. Oh well, I'd say practice and just keeping up memorazation. Like give yourself a script (get a book of little scripts) and try to memorize one a week. (learn it in an hour) like five lines. I always hop up and down before I go in the room to do my stuff. That helps, it gets the jitters out some. I also take a moment to close my eyes and when I open them I become the character.

You have two problems on your to handle your first one you must read consistently over and over and over and for the other try preforming in front of a small stage until it gets bigger and bigger