These are the commands that I look up the most to make sure I'm doing them right. Eventually I'll remember them…

This will create the new branch. When the branch is created, it will be active with the changes from the old branch. Switching back to the old branch will no longer show the changes.

$ git checkout -b <new branch>

Commit any local changes then:

$ git push -u origin <new branch>

$ git branch -D <branchName>
Deleted branch <branchName> (was ....).

$ git push origin --delete <branchName>
To git@github.com:<repository>.git
 - [deleted]         <branchName>

Merge branch into current branch

$ git merge <branch>