When I ordered the ALIX.3D3 board I thought installing Gentoo on this should be a piece of cake, but finally there were some stumbling blocks and that's why I want to summarize how I got gentoo running.
First of all, I recommend installing Gentoo on a normal desktop to get to know the installing process, which is a bit different from graphical installers of mainstream distros. The Gentoo Handbook is a great documentation how this done.
To install gentoo, you have to boot a minimal or "rescue" linux usually from cd/dvd. I tried to convice the bios to boot from a usb cd-rom drive, but I hadn't any success.
So I had to prepare a USB stick to boot from. There's a nice tool UNetbootin which automatically copies ISO images to a usbstick and makes it bootable. I tried a lot with the Linux version of it but didn't had any success regardless of which ISO image or USB stick I took. So I booted windows and tried it with this version. I had success on the first attempt, using the install-x86-minimal.iso from Gentoo and a 3 EUR SD-card Reader with a 4 GB SDHC card in it, formatted as FAT32 as the only partition (not in superfloppy mode).
If you've got a booting usb stick, insert it into a USB plug of the board, attach a USB keyboard and a monitor to the VGA port. Power on and press escape to select the boot menu. There should be an option for the usb stick if everything went fine.
Now the gentoo minimal system should boot and you can proceed with the usual installing (look into Gentoo Handbook for details). The AMD Geode LX800 cpu is a i586 cpu, so you have to install a i386, i486 oder i586 stage (i686 or amd64 won't work!). I installed a i486 stage 3 and updated later to i586.
Partitioning should follow your preferences but don't a forget a swap partition. 256 MB of RAM is not that much and gcc will not compile without!
CFLAGS="-O2 -march=i486 -pipe"
for installation as the gcc version on the stage3 archive don't support the geode march.
The rest of the installation is business as usual. I installed gentoo-sources for a optimized kernel and took this configuration here: ALIX.3D3 kernel-2.6.29-r2 config
After finishing installation and booting with the new kernel, it's time to update the systems to i586. For this, at first update all packages to actual version, especially gcc to version 4.3. Afterwards it's save to change
CFLAGS="-march=geode -Os -fno-align-jumps -fno-align-functions -fno-align-labels -fno-align-loops -pipe -fomit-frame-pointer"
and proceed with changing of the CHOST variable. There's a nice tutorial here: Changing CHOST.
Now you should have a nice and optimized gentoo on your ALIX.3D3