I recently wanted to make a copy of a github project. It sounds like I basically want a fork but, as of November 2010, github does not allow you to fork your own project. I think the following steps are currently the most straightforward to copy a project.
First, I setup a new project on github.com, let's call it "new_project_name". Let's call the original project "old_project_name". I will also refer to my github username as "github_username".
After new_project_name was created on github, I ran the following commands:
cd some_temp_dir
git clone git@github.com:github_username/old_project_name.git
mv old_project_name new_project_name
cd new_project_name
git remote rm origin
git remote add origin git@github.com:github_username/new_project_name.git
git push origin master
cd ..
mv new_project_name ~/my_usual_workspace_area
Now the cloned project is detached from the original and I can work on them independently.
In my situation, I was actually splitting a single project into two projects. Maybe in this case it made more sense to copy the project than to fork it, because I don't expect to ever merge the copied project back into the original.