First of all, you don't need to do this is-store, unless you for some reason want to make a trip there. Instead, you can do this in an online chat at AT&T's website.
The only info AT&T requires is the IMEI number of your iPhone, which can be found under Settings > General > About in iOS. The process to initiate the unlocking takes only a few minutes.
Notably, some have said they have seen the delivery of the code within minutes, whereas others were quoted that it might take as long as four to six days.
A few other details: the maximum number of devices that can be unlocked in a single year is 5. Multiple simultaneous device unlocks must be submitted through AT&T customer care. As noted before, you must have completed the two-year service agreement.
Also, if your iPhone is used, AT&T will check the account history of the original owner to ensure that the contract has been completed.
This is the same process that occurs in the rest of the world, so none of it should be a surprise. If anything is surprising, it's that AT&T has finally done this (although it's probably because of increased competition from Sprint and Verizon).