There are several methods to installing XBMC to Ouya, and this page describes an "Out-of-the-Box" method.
Step 1: First go to the developer section (the Make tab) in Ouya, select Yes or "okay" to enter the developer section.
Step 2: Open the default browser and then press Y on the controller to enter in your own URL.
Step 4: The download is 50.3 MB and depending on connection can take a while, during the download you won't be able to tell the progress unless you have installed Chrome or ES File Explorer.
(If you have ES File Explorer you can just open after it finishes and install).
Step 5: Once the download completes, navigate to the Manage tab -> System -> Advanced.
Step 6: Select Storage and then scroll down to Downloads.
Step 7: There will be a list of all the downloads, select the XBMC download and click install.
Step 8: ...and you're done! XBMC will be under the Make tab.