After receiving instructions from ATT, follow them. I just did this in June, so I know what I am talking about.
Here are some notes I took for my daughter to help her unlock:
1) Sync your phone (very important because iTunes does not back up your contacts and you want the latest data when you backup/restore)
If you have a lot of apps, take screen shots of each of your screens - when your apps are restored, they are scattered all over the place.
2) Right click your phone in the left side column of iTunes and select "Backup"
3) With your phone still connected, after Backup is successful, On the Summary tab in iTunes, under "Version" click "Restore"
You will get a warning that all data and settings on your phone will be wiped out
The process takes about 15 minutes
When it's done, you get a message that your phone has previously been connected to "this" computer
And you will be asked if you want to restore from backup - YES you do
You may or may not get a message from iTunes that your phone has been unlocked. I did not get it, but did get a text from ATT that it was unlocked. I called just to verify anyway.
After that restore, you need to right click on your phone in the left side column and select "Restore from Backup" to get your data back.
Sync your phone again to get your contacts back.
The restore is what unlocks your phone, as the unlock is in the update provided by Apple after ATT has told them your IMEI is eligible for unlock.
Disregard any info about changing sim cards. This is no longer true in the US for ATT. Apple is now in complete control, and no new sim is needed. I do not know why Apple has not updated their doc.