Wow, everyone jumped in and gave such great advice already. Not much for me to add except that PA Steve is correct. Book the excursions through the TV system in your cabin. Don't waste good cruising time standing in a line.
I almost echo the advice on booking your first cruise excursions through the ship. It does give piece of mind to those who are new. BUT, if you wanted to save some money, the place to try booking your own would be Grand Cayman. They are very easy to do there and all the tour operators pick up right there where the tenders drop you off (with all the ship booked excursions) Captin Marvins seems to be the favorite here, so look them up on the internet and reserve a spot. You can save some money and gain some experience in booking your own at almost no risk. (Most of their customers are booked through the ship anyway so you will be back in time for the departure. Just make sure you leave a couple of hours of "buffer" time on the return and make sure your watch is set to SHIP time. Not local time or you can be an hour off..
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
NCL Dream October 2006, RCCL Mariner OTS June 2007