Hey, so I called and talked to some folks and they said they have a brand new process for trade ins and it looks like this:
When you initiate your trade in online you'll get an initial email (Important step before you trade in your device.) this email tells you how to prepare your device as well as some of the info about the trade in such as the device you're trading in and how much you were quoted for it's value.
Now, you'll need to wait because there's actually an additional email coming (my 2 emails were about 30 minutes apart). This email subject line will be something like "Your trade-in has been initiated". This email will have the information about where you can drop off your device (in my city these are FEDEX locations, and I suspect this is the case in other cities too HOWEVER not every fedex location is a participant so be sure to check that link to see who is and isn't), how to prepare your device in case you haven't already from the previous email, a QR code that FedEx will need to process your drop-off and information about your trade in device.
The drop off to FedEx is going to be the easiest and fastest for most people. Print out this email with the QR code and bring it with your device. You don't need to package it up and you don't need to pay for shipping!
If you do not want to drop off at a FedEx location you'll need to call 1-800-MY-APPLE to request they send you the trade in shipping kit OR you can bring it to your nearest Apple Store if that's an option.