You can buy wireless minute packages. When I was on the Conquest last year I checked email and chatted with work twice and there was about a $10 charge on my sign and sail card. This year I am bringing my Verizon internet card and hoping to bypass the charges.
Our Verizon wireless card hasn't worked on any of the Carnival ships that we have been on. Neither did our other aircard. Not sure what was up with that but I wasn't very happy. Good Luck! The way that I look at it, even with the premium prices charged for the internet onboard, it's still far cheaper than calling home using either the ship phone or the cellphone.