(Full disclosure: I consider myself still rather new to Git and VC systems in general, even though I have used them from time to time.)

Considering your question, you may want to refer to the "Integration-Manager Workflow" workflow in Scott Chacon's book, Pro Git, with an eye to using your GitHub repo as your "blessed" (golden?) repository (that anyone else wanting to work on the code pulls from), and your local repo as the "integration manager" repo illustrated in figure 5-2.

(I also have tried to start using Vincent Driessen's branching model, with the idea that the master branch (and possibly the develop branch) would available in the "blessed" repository as working code.)

Hope that helps.