Once you get the confirmation email you simply need to insert a non T-Mobile SIM card to complete the unlock. You will see the other carrier up where the signal bars are.
In many cases, just a few hours after making the unlock request (even before receiving the confirmation email) the device is unlocked. Apple is fairly quick about their device network unlocks (for the most part).
It's recommended (not required) to back up your device. I recommend it personally. What may happen which has been rare in my experience: is that you may have to connect your device to iTunes to complete the unlock. But again, that has been a rare occurrence in my experience.