It's very simple:
To delete the remote branch
git push -d origin <branch-name>
Or
git push origin :<branch-name>
-- You can also delete tags with this syntax
To forcefully delete local branch
git branch -D <branch-name>
Note: do a git fetch --all --prune on other machines after deleting remote branch, to remove obsolete tracking branches.
Example
to remove local branch
git branch -D my-local-branch
to remove remote branch
git push origin :my-remote-branch
Happy Coding :)
