To delete any branch, you shouldn't be on that branch, so switch to another branch before giving the commands
To delete any branch run,
git branch --delete <branch_name>
or
git branch -d <branch_name>
But this fails if the branch hasn't been merged, so to force delete, if required, run,
git branch --delete --force <branch_name>
or
git branch -D <branch_name>
To delete the remote branch, you need to run,
git push origin --delete <branch_name>
or
git push origin :<branch_name>