You will need an SD card of 1GB or more, a USB disk/key of 4GB or more (the target device you install to, if you want to install to the SD you run the installer from, use the NetInstall image) and a powered USB hub.
Download installation software
Download the ubuntu-10.04-netbook-armel+omap.img image file from http://cdimage.ubuntu.com/ports/releases/lucid/release/
Write the image file to an SD card:
sudo dd if=/path/to/img/file of=/dev/mmcblk0
Attach your display and a keyboard to the Beagle Board.
If your NAND setup is still the default that was shipped with the Beagle Board you can boot now.
In case your uboot setup is not able to boot a boot.scr file anymore, use the following uboot commands in a serial console to boot from the Ubuntu SD card:
OMAP3 beagleboard.org # mmc init OMAP3 beagleboard.org # fatload mmc 0 0x82000000 boot.scr ... OMAP3 beagleboard.org # source 0x82000000
After kernel and initramfs were loaded from the SD you will be presented with the ubuntu live installer screen on the attached DVI display.
Just follow the installation process, at the end you will have a fully working Ubuntu netbook installation on your beagleboard.
Live image usage
If you quit out of the installer, the image can be used as a decent live image of the netbook UI.