Welcome! Thanks for your interest in contributing to api.jquerymobile.com. You're almost in the right place. More information on how to contribute to this and all other jQuery Foundation projects is over at contribute.jquery.org. You'll definitely want to take a look at the articles on contributing documentation.
You may also want to take a look at our commit & pull request guide and style guides for instructions on how to maintain your fork and submit your code. Before we can merge any pull request, we'll also need you to sign our contributor license agreement.
You can find us on IRC, specifically in #jqueryui-dev and #jquery-content should you have any questions. If you've never contributed to open source before, we've put together a short guide with tips, tricks, and ideas on getting started.