If you have better luck than I, you may be able to install Ubuntu 8.04 from a USB stick. If you read my previous post, you'll know that I can't get that to work.
So here's what to do: beg, buy or borrow a USB2 DVD drive. (I went with "buy"). The helpful guy at the Future Shop sold me a LG 20X Super Multi External DVD Rewriter (GE20), which just happened to be the cheapest USB2-optical device available in my area of the city. He warned me that some computers' BIOS' support booting from USB2 drives and some don't. Given that the eeePC comes with a recovery DVD and support CD, I assumed that it was able to boot from an external optical drive. This turned out to be correct.
So, I booted from the Xubuntu 8.04 Live CD, and lo and behold, the eeePC boots! (It refuses to do so with almost all of the USB drives I tried to create.) Up comes the load screen, and then the Live session begins. I chose to install Xubuntu. I won't go into the details here, because the install failed. I think, in retrospect, this is because I chose to change the partition setup, but I did not click the little "format" checkboxes in the installer. Whatever the reason, the installer fails due to an unspecified I/O error at 53% into the install process (This happened twice in two attempts, at the identical point.)
So I tried booting from the Ubuntu 8.04 CD. The only difference here is that Ubuntu uses the Gnome desktop, and Xubuntu uses the XFCE lightweight desktop.
The Ubuntu live session booted, and I started the install. When asked how I wanted to partition the drive, I chose "manual". In its stock (Xandros) configuration, the drive has 4 partitions on the fast 4Gb motherboard-mounted hard disk and two on the slower 16Gb removable hard disk. The first thing is to select "new partition table" for each drive. For the 4Gb drive, I created one partition, in the ext2 format. The "mount point" is "/", to indicate that the root of the filesystem goes in that drive, with all the system files. Be sure to check the "format" checkbox to ensure that the drive is wiped before installing, as I think omitting that killed the Xubuntu installer. For the 16Gb drive, I made one partition, in ext3 format, mount point "/home", to indicate that the user's files will go on this drive. Again check the "format" checkbox. When you accept the configuration, it will warn you that you have not allocated any swap space. This can affect performance when you use a lot of RAM, but using the SSD drives for swap space can reduce their lifetime, as they have a finite number of writes before they die. I hope the system can function well without swap. We shall see. It also warns that this will wipe any files on the drives. I don't have anything of importance on my machine, but if you do, then don't hit that button until you copy your files somewhere safe.
The rest of the installation went fine. I was worried that Gnome would be too resource-intensive for the eeePC but it runs well, even with some of the graphical effects turned on. I will detail the setup later once I have it working, but suffice to say that within an hour of installing Ubuntu, I had working Wifi, Ethernet, custom keys on the keyboard, installed build-essential, got the camera working, and installed subversion and GTK.
Now that Ubuntu is installed and configured, it's like night and day. I will never go back to the default Xandros OS.