SHELL

how to push code to another remote git repository

git remote rename origin upstream
git remote add origin URL_TO_GITHUB_REPO
git push origin master

git push to another repository

Create a new repo at github.
Clone the repo from fedorahosted to your local machine.
git remote rename origin upstream
git remote add origin URL_TO_GITHUB_REPO
git push origin master
Now you can work with it just like any other github repo. 
To pull in patches from upstream, 
simply run git pull upstream master && git push origin master.