How do I copy text from my xterm without a mouse?

You can use GNU screen’s copy and paste commands.

Quick tutorial:

1. Open screen: screen (or screen myprog my args here)
2. Run your program, producing output you want copied
3. Enter copy mode: Control+a+[
4. Move your cursor to the start point
5. Hit Enter
6. Move your cursor to the end point
7. Hit Enter
8. Paste: Control+a+]

Screen is much more powerful than that (I use it to tab several virtual terminals without the need for a special terminal emulator, and also so that I don’t loose my sessions when X crashes or something). To get out of screen, simply end your shell session, or type Ctrl+a, Ctrl+\.