The common model for contributing to an open-source project is the fork/pull request model. In this model, if you want to contribute to a project, you don't need commit rights to the projects GitHub repository. Instead, you "fork" the repository to create your own copy. You make your changes in your own fork and then submit a "pull request" (PR) which is a request that your changes get merged into the main repository. The fork/PR model is beneficial even in a work environment, as it allows fine-grained control over repository permissions while still allowing non-owners to contribute. See GitHub's About collaborative development models and its "Further reading" section for more information.
This document gives some tips for: