Dave is correct about the taxi service. The only thing I would add is that if you do a Priceline or a Hotels.com booking, you will see them mention a port shuttle if they offer one. Just be careful about spending extra on a hotel because it offers a shuttle when a taxi ride may only be $20 with tip (depends of course on how far away the hotel is) Also make sure you know if it is "offered or available" (that means they typically charge for it) versus "provided or free"
I normally call the hotel before I book to verify and then to find out if I have to reserve shuttle space ahead of time.
Now, having said all that about shuttles... a taxi may still be preferred since you don't have to wait for a taxi, you can go anytime you want and sometimes the shuttles are mini buses and you have to wait for everyone going on that round to get to the bus and board etc etc... you don't have that hassle with a taxi. I would book a hotel close to the port and then ask for a taxi at a given time and pay the $20... Unless there are more of you than could fit in a van taxi.
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise, Magic 1/14
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013