Unlocking an iPhone modifies the device so it can be used with any SIM card. If inserting a SIM card into the device produces an "Insert SIM card with no PIN lock" error, the unlock was performed incorrectly. Re-insert the AT&T SIM into the iPhone if you don't want to void its warranty or your AT&T agreement.
Disconnect the iPhone from iTunes. Push the end of a paper clip into the hole next to the iPhone's SIM tray and push it in.
Remove the SIM tray from the iPhone. Push out the third-party SIM card and set it aside for later use.
Insert an AT&T SIM card facedown. Replace the SIM card and press it back in. Wait for AT&T's name to reappear in the upper left corner of the screen.
If a Verizon iPhone displays an "Insert SIM Card" error of any kind, discard it. Verizon iPhones use CDMA technology, and doesn't use a SIM card.