Phil Sturgeon has posted a guide to his site about running tests and contributing back to packages that live in Composer.
While Composer has been around for a while now, many packages are still in their infancy (< 1.0) or sometimes are just not as feature filled as they could be. To be fair there is always more to be done. It can always do more, or do the same thing more efficiently. Whatever the case, pull requests are going to be a common thing for the PHP community to be doing to these packages and this needs to be done safely, with unit-testing. So, how do you run their test suite and add your own tests?
He includes a step-by-step guide to getting the environment set up to run the package's tests and how to add some of your own. He includes the commands to send the pull request back up to Github (on your own fork, of course) and how to use that same fork as your package resource until the main project is updated.