The best way to book a suite is to call the captain. He will set you up with the cruise director, unless of course you want the Owners Suite and he will forward your call to the owner of Carnival.
Booking a suite is no different than a inside, outside, or balcony. You can use a TA, Expedia, Carnival or like I do a personal travel secretary. The secretary is the easiest. All I have to do is show up and leave her with all the details.
Be sure to ask for the Owners Suite. They are a big improvement over those small standard suites. The perks and service is a notch higher and you basically get first choice at everthing. You never have to stand in a line or not have a seat.