On the project page (http://github.com/you/project) there will be a link on the right at the bottom of project tools list with a path to a .git repo
Open a terminal and type:
git clone [link to repo here]
That will create a local clone of the repo you can work on, then if you follow the instructions on GitHub to add a remote server you can push your changes back.
Syncing files back and forwards is just as easy;
Computer A (Had the original git repo)
Computer B (Has the cloned repo)
Make some changes on Computer A, then run
git push origin master
Go to computer B, then run
git pull origin master
To sync your new changes, make some changes on computer B then push back
git push origin master