I just recently installed ubuntu on my new chromebook and figured I would detail my experience. I started by just googling it and finding a couple of different methods. The easiest one seemed to be using crouton, a chroot generator for the chrome os. I went through the steps and found out that there are really a few different flavors of linux that can be installed, and of course I didn't get ubuntu. It took me a couple of try's and I finally got the right one. So, with that said here are the steps to get the desktop version of ubuntu running on your chromebook.
Step 1: Enable Developer Mode
Each chromebook has possibility of having a different method for booting into dev mode, but for mine (Acer Chromebook 11), I simply had to hold down Esc + Refresh and press the Power button.
Quick thing to note is that by doing this, your chrome os will be wiped. No worries though, all of your information is synced via your google account and will be re-downloaded by the main os setup.
Once your chromebook reboots, simply wait for the recovery mode screen and press Ctrl + d to start the developer mode setup. It took roughly 3-4 minutes on my system.
Once this is complete, you'll want to login to your chromebook like normal. One thing to note is that from now on when you boot up your chromebook you'll see the recovery screen and will have to press Ctrl + d to get into your system. Kind of a pain, but well worth having ubuntu installed. Ok, so once your in the chrome os, you'll have to go through the intial setup again.
Step 2: Install Crouton
You can either head over to the github page or download it directly. Once it's downloaded, open up chrome and type Alt + Ctrl + t. This will open up a terminal window in chrome and we can get started. Now type the following commands:
shell sudo sh ~/Downloads/crouton -t unity
This will download and install ubuntu on your machine. Be patient as it can take a while depending on your internet speed. Once it is all finished go ahead and run:
This will boot your system into ubuntu.
If you are currently in ubuntu, you will need to either logout, or press Ctrl + Alt + Shift + Back to switch back to the chrome os. To switch to ubuntu from the chrome os you need to press Ctrl + Alt + Shift + Forward and then run:
chronos sudo startunity
Hope that helps, Enjoy!