gitt clone one repo and push to another code example

Example 1: git push new repo to remote

$ git remote add origin <remote repository URL>
# Sets the new remote

# Push the changes in your local repository to GitHub.
$ git push -u origin master
# Pushes the changes in your local repository up to the remote repository you specified as the origin

Example 2: 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.