They send via FedEx for stuff within the continental US, and USPS for International stuff.
Generally speaking, once they've received the order, you won't hear back unless there's a question in the shop. If you gave your email on order, you'll get a shipping confirmation email. Otherwise, it'll show up on your doorstep about 12-14 weeks from the order date.
Again, this is speaking in generalities, and how it was before I left. I know they're very busy this time of year, and when I stopped in earlier this week, they're all working very hard and happily. Stock show is a great time for them. They've got a new guy on staff (essentially my replacement) who's VERY good at what he does. Wouldn't get a hat anywhere else!
But yeah, as Michaelson said, if you have any concerns, just give the shop a holler from the 1800 number on their webpage.