While github recommends that branches be made locally, I prefer the data security of keeping them off-site.  This is how to manage and merge a branch that's kept remote, on github.

https://github.com/Kunena/Kunena-Forum/wiki/Create-a-new-branch-with-git-and-manage-branches
https://try.github.io/levels/1/challenges/19
http://stackoverflow.com/a/6232535

Checkout a new branch on your computer (this is not something on github)
git checkout -b <branch>
Push the branch to github - now there's a new branch up there.
git push origin <branch>
And to switch to a different branch, use
git checkout <branch>