Do I use the box I got my new phone on?

You will receive a special box to send the device back in. Mine came through UPS and after following instructions for using the box, I simply dropped it off at the nearest UPS facility. My box arrived about 2 weeks after the purchase. I imagine they are very busy now.

If you arranged the trade online when purchasing the new phone, the box and instructions for returning it should arrive soon (possibly 3 or 4 days) after your new phone.