First make a backup of your present system. That is *essential* because if things don't work according to plan, you will need to reinstall to factory standard.
Next, do a search on the Internet for a version of Ubuntu that was designed for the Asus Eee.
Load that on to a USB stick and make it bootable. Sorry, but you're going to have to search for that information.
I've seen Ubuntu running successfully on an Eee - complete with a full implementation of Compiz, but whether it will run on a One, I don't know.