Please note, this process will root your Ouya console and install several applications. If your Ouya is already rooted you can just install the included xposed-ouya-plain-purchases-1.1.0.apk and enable it in Xposed Installer. The included script removes Busybox, Superuser, and Xposed Installer before attemping to install them to make sure the correct versions are running.
Watch the entire video to see how the process works and the end result before running the script on your console. This will not work on 100% of the paid games and applications as some of the developers did not use the Ouya API purchase model and used their own servers for validating purchased apps.
Things You Will Need
Prerequisites and Downloads
Running the ADB Script
Enabling Plain Purchases
I cannot thank Christian Weiske enough for reverse engineering the Ouya API and purchase process and hosting a static recreation of it so Ouya's around the world can continue to work. Show Christian some love at https://ouya.cweiske.de
Ouya Plain Purchases: https://github.com/cweiske/xposed-ouya-plain-purchases/releases
Further reading: http://cweiske.de/tagebuch/ouya-purchases.htm