We have a miniature schnauzer. I never dreamed that we could fly with him until we saw one on our last flight. They had a small carrier which I didn't even know existed. After checking I found them--even at WalMart. It looks like a small carryon bag but has mesh to allow the air to circulate. As long as it is a small pet--it's just treated as a carryon.
I have never flown with my dog but I just learned from my friend who is currently on a plane with her dog that you do need medical clearance for your dog from a vet. I think the certificate has to be given within a certain number of days of the trip.
Fiver is right - you have to get clearance before you can fly. Tell your vet that you're flying and he/she will give you what you need. When you check-in at the airline, you'll show the form (that the vet gives you) and pay $50. Make sure you have a bag like Liketeaching was talking about - the airline will tell you what size for their plane. If you get the mesh one, you can be sure it'll fit because the top will "squish" down if needed. I put Daisy under the seat in front of me so I could see her, and she did fine! I think the rumbling of the plane puts most of them to sleep. I did take her out of the carry-on when we were in the airport, but I kept her in my lap.
I think we flew with Delta (it was 2 years ago), but I would call your airline ahead to make sure of what their policy is.