To delete a repository in GitHub, follow these steps: 1. Go to the main page of the repository you want to delete. 2. Click on the 'Settings' tab located on the right side of the page. 3. Scroll down to the 'Danger Zone' section. 4. Click on 'Delete this repository'. 5. Read the warnings carefully, as this action is irreversible. 6. Type the name of the repository to confirm you want to delete it. 7. Click on 'I understand the consequences, delete this repository'. Make sure you have a backup of any important data before proceeding with deletion.