If you KNOW you want a particular excursion go online to CCL's site, log in with your reservation number and reserve the excursion you want. That way you know you will be able to get it. They will bring the tix to you cabin the night before that port and charge it to your sign and sail card. If you do not know which excursions you want, or you are undecided, my advice would be to attend the "excursion chat" which is normally planned the first day before you get to the first port. They will go into detail of each excursion and you can better determine if you want to go on them or not. Then, instead of going to the excursion desk, go back to your cabin and use the TV system to book excursions. OTherwise you will be waiting in a long line at the desk.
Lastly, you could always "do it yourself" and arrange your own excursions, but that might be a bit much for a first time cruiser. If you want to try this, go online and search for tours for each port of call. You can find tour companies (probably the same ones that work with CCL) that you can book tours through.
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