Pick the name of a Distro and search in Google..
for instance 'Debian EeePC' gets you a link to
http://wiki.debian.org/DebianEeePC/HowTo/Install
There are quite a few different Distros that should work on that unit, since Asus was the first out the gate with the netbooks after all.
If you look at
this post you will see the various Distros I have found that work on the Acer Aspire One Netbook. I would imagine most of those Distros will also have how-to pages for the ASUS EeePC units.
Also eeeuser.com has a wealth of info on the EeePCs, such as this list of custom Linux distros, and standard Distros on the EeePC.
http://wiki.eeeuser.com/#installing_operating_systems
I guess a better questions would be "Which distro will NOT work on a EeePC ?"