You will use the command --sign-key to put your signature below the key. As you need to use you private key, you will be asked to type the passphrase.
Afterwards, you might want to export the signed key again and give it back to the owner. He can import this key again and your signature will then also show up in his public keyring. Whenever he exports his public again, your signature will be included and tell others, that you trust him.