The Aura Framework project has made a new post to their blog walking you through the steps you'll need to contribute back to the project with your ideas and bugfixes for their various components.

Sometimes you may have noticed a bug, or need a feature implemented, and need to contribute back to the aura community. These are some of the steps to help / contribute to aura project.

They walk you through: setting up git (well, point you to github's guide), fork the main repository and check out a copy, creating a remote to the "upstream" (main) repository and pulling the latest content from it into your fork. Included are the commands to run PHP_CodeSniffer and PHPUnit with the provided tests. From there, it's up to you and your code to contribute back, commit and make a pull request!