After my phone was paid off I called AT&T to unlock my phone. They emailed me a url link that requested some details like IMEI for my phone and then I submitted my request. Got email confirmation that they were working on my request. A few days later I was emailed instructions for how to unlock my phone which went something like this:
1. Get a non-AT&T sim card
2. Insert sim card into phone
3. Restart phone
4. When prompted enter code*
5. Code is accepted and phone is now unlocked
*Code is unique and emailed along with the instructions
Good luck