To delete a local git branch:

git branch -d <branch_name>
git branch -D <branch_name>

-d corresponds to --delete, which will only delete the local branch when all local commits/merges have been pushed to remote while -D expands to --delete --force.

To delete a remote git branch:
git push <remote_name> --delete <branch_name>

This will then often require on other machines to update the local list of branches git remote update <remote_name> --prune

…in most cases, >remote_name> is origin.