To delete a Git branch both locally and remotely, you can follow these steps:

Deleting a branch locally:

1. Open your Git repository in a terminal or command prompt.
2. Verify the list of branches and make sure you are on a different branch than the one you want to delete. You can use the command git branch to list all the branches and see which one you are currently on.
3. If you are on the branch you want to delete, switch to a different branch using git checkout <branch-name> or create a new branch to switch to.
4. Once you are on a different branch, run the command git branch -d <branch-name> to delete the branch locally. Replace <branch-name> with the name of the branch you want to delete.
5. Git will check if the branch has been fully merged into other branches. If the branch has been merged, it will be deleted. If it hasn't been merged, Git will display a warning message. If you still want to delete the branch despite the warning, use the command git branch -D <branch-name> instead of -d.

Deleting a branch remotely:

1. After deleting the branch locally, you can delete the remote branch as well. To do this, use the command git push origin --delete <branch-name>. Replace <branch-name> with the name of the branch you want to delete.
2. The command will remove the remote branch from the Git repository. If you have the necessary permissions and the branch exists on the remote repository, it will be deleted.

It's important to note that deleting a branch is a permanent action, and once deleted, the branch and its commit history cannot be easily recovered. Therefore, exercise caution when deleting branches, especially if they contain important or unrecoverable work.