The Concept of "patching" is a little different with Github and Git. If you've never used Git before, you might need to brush up a bit on it. Once you do it, however, it's very, very simple and extremely helpful!
Getting to Know Github
This screencast will walk you through all you need to know to get working with Github and Git. It lasts about 10 minutes or so and you'll learn a bunch of new stuff!
Github Issue Tracker Integration
Additionally, you can follow the convention of appending "Closes #1" (where 1 is the issue number) to your Commit messages. Github will automatically mark that Issue as Resolved!