badgerports is an Ubuntu repository. In order to use it, you must add it to your Software Sources.
Click on the "Ubuntu Software Centre" icon in your Unity dock, or via the Dash button.
Click on "Edit", "Software Sources".
Click on the "Other Software" tab.
Click on "Add...", and enter the line:
deb http://badgerports.org precise main
Click on "Add Source"
Click on "Authentication", then on "Import Key File"
Download this GPG key file, ID 0E1FAD0C, and select it in the "Import Key File" window
Click on "Close". You're all set!
From now on, whenever you try to install or update Mono-related packages on your system, you will be given the badgerports version for preference. You don't need to do anything more than update your system as usual to get started!