How does my recovery contact obtain the code to give me to recover my phone?

See instructions in Help a friend or family member as their account recovery contact - Apple Support

As explained in Set up an account recovery contact:

"How to get a recovery code from your recovery contact

If you forget your Apple ID password or get locked out of your account, just follow the steps on your device to share the onscreen instructions with your recovery contact in-person or on the phone. Your recovery contact then shares a six-digit code that you enter on your device. After your identity is confirmed, you can reset your Apple ID password."