As promised, Canonical has released a tool that lets you install Ubuntu Linux on the Google Nexus 7. Cleverly enough, it's called the Ubuntu Nexus 7 installer, and it's a relatively simple tool that you can use to install Ubuntu 12.04 on the 7 inch tablet.
In order to use the installer you'll need a computer running Ubuntu, a Nexus 7 with 8GB or 16GB of storage, and a USB cable to connect the tablet to your PC.
You'll also need to unlock the bootloader on your tablet. If you haven't already done that, it'll wipe all the data from your device. So proceed with caution.
Installing Ubuntu will also wipe your device — so if you plan to go back to Android, you'll probably want to make a backup using TWRP or ClockworkMod, then copy that file to your PC or an external storage device for safekeeping. That way you can re-install Android (following Canonical's instructions), re-root your device (following ours), and then re-install ClockworkMod or TWRP to restore from your backup and get your Nexus 7 back to where it was before you started.