1. Delete the relevant section from the .gitmodules file.  The section would look similar to:
```
[submodule "vendor"]
	path = vendor
	url = git://github.com/some-user/some-repo.git
```
2. Stage the .gitmodules changes via command line using:
```
git add .gitmodules
```
3. Delete the relevant section from .git/config, which will look like:
```
[submodule "vendor"]
	url = git://github.com/some-user/some-repo.git
```
4. Run git rm --cached path/to/submodule .  Don't include a trailing slash -- that will lead to an error.
5. Run rm -rf .git/modules/submodule_name
6. Delete the now untracked submodule files rm -rf path/to/submodule