Create a branch:
$ git branch <name_of_your_new_branch>
Push the branch on github :
$ git push origin <name_of_your_new_branch>
Switch to your new branch :
$ git checkout <name_of_your_new_branch>
When you want to commit something in your branch, be sure to be in your branch.
You can see all branches created by using
$ git branch
Which will show :
approval_messages master master_clean
Add a new remote for you branch :
$ git remote add <name_of_your_remote> <url>
Push changes from your commit into your branch :
$ git push origin <name_of_your_remote>
Delete a branch on your local filesytem :
$ git branch -d <name_of_your_new_branch>
Delete the branch on github :
$ git push origin :<name_of_your_new_branch>
The only difference it's the : to say delete.
If you want to change default branch, it's so easy with github, in your fork go into Admin and in the drop-down list default branch choose what you want.