Carnival uses the Mears Bus company as its method of transportation to Port Canaveral. The cost is $15 one way, $30 round trip. You can purchase these tickets right at the airport from one of the Carnival representatives. They will be waiting around the baggage claim area, holding a Carnival sign, and will direct you to the busses. If you don't see these people, Mears also has a ticket booth in this area as well. The busses are modern motorcoach-type and are very nice. We used them earlier this month for our cruise on the Pride. The trip is almost an hour, so they provided a movie during the ride. If you prefer a limo/towncar type method of transportation, I recommend the Tiffany Towncar Service (www.tiffanytowncar.com). This way is considerably more expensive, but it is a very nice and well-run company. We used them for our Disney trip this past summer, and we did inquire about using them for a cruise. I don't remember the actual cost, but I believe it was over $100 for a round-trip ride. They will email you a quote if you inquire with them. (ask for Moe, he's great!)
Hope this helps!
We went a day early and got a shuttle with Omni Trans in Orlando. They were prompt in picking us up at the airport and at the port. We paid 110.00 for six of us round trip. We took the Mears shuttle the year before and it was ok if you don't mind the herd of cattle thing. I prefer the private shuttle.