It's simple. I'll show on one example.

I was interested in Sphinx search server, so I've decided to do its protocol implementation in javascript (for node.js).

I've created project on github and got remote URL. Then I've created folder on local disk and started coding. Reverse-enginereed PHP Sphinx connector, written some JS code, commited it to local Git repo. Next step: add remote URL to git repo. After this I can push my changes to Github with "git push remote master", where "master" is the branch name. And voila, project is on the Github.

Then I write some more code and get first working prototype. I announced it in node.js Google group to attract another developers to project. They watch, comment on commits (not often) and send pull requests for code via Github (more often). Then I decide if I need the patch and apply / modify+apply / decline patch. Someone can fork my project if they feel I won't add some feature they need or I'm too lazy updating the code.

Basically, that's it.