The answer to 'how to unclog shut-off valve' is to first try to manually turn the valve to open it. If the valve is stuck, you can try using a plumber's wrench or channel-lock pliers to grip the valve and turn it. If the valve is still stuck, you may need to replace the entire shut-off valve.
It's important to shut off the main water supply to the home before attempting to work on the shut-off valve. This will prevent water from leaking out while you're trying to fix the issue. If you're unable to get the valve unstuck or need to replace it, it's best to call a professional plumber to handle the job.