The Arduino site has eeePC-specific instructions for setting up the Arduino environment. It turns out to be as simple as installing a few packages and then uncompressing the Linux Arduino software. Just follow the links:
The Arduino Download page.
Arduino for Linux instructions.
Arduino for eeePC Xandros Linux instructions.
Note: while the instructions say to use the Debian repositories to get your packages, it is better to use the Xandros repositories. If you have not already, go back two entries in this blog to see how to set this up.