With your days spent either on the boat or in one of the ports, the majority of the clothes you will be wearing are casual clothes. These clothes take up the least room in your suitcase and will serve you well. Depending on the number of days of your cruise, you should plan on having several pairs of shorts or capris, at least one more shirt than the number of days you are on the cruise, and one or two bathing suits. A good example for a seven day cruise is eight shirts (A mix of button down, loose Hawaiian type shirts and tee shirts work), three pairs of shorts or capris and two bathing suits. There are no irons allowed on cruise ships, so make sure you pack things that won't wrinkle easy.
Carnival Cruise ships have a dress code for dinner in their dining rooms. This dress code amounts to a business casual look. For men, this means slacks and a collared shirt (think golf or church clothes). For women, this means casual dresses or capris and a nice blouse (Jeans are not preferred). Also, Carnival usually has one or two "formal" nights where men are required to dress in a suit or tuxedo and women should wear a formal dress. These items will take up room in your suitcase so pack accordingly. A good estimate of things to bring on a week-long cruise is three pairs of slacks, four polo shirts, two dress shirts with tie, and one suit for men and three or four nice dresses for women.
The biggest part of your packing will be the space your shoes take up. Luckily, this is also an easy fix. Focusing on the casual theme makes it really easy to choose shoes you will be bringing. For lounging about on the ship, all you will really need is a pair of sandals. They are perfect from getting to and from the pool area and ships aren't so big that you'll need more support. On days where you will be in port, a good pair of tennis or walking shoes will do the trick. For the formal dinners, you will need a nicer pair of shoes to go along with your outfit. Men can usually get away with one pair of dress shoes and women will need two or three pairs to round out their outfits. A good idea for shoes is one pair of sandals, sneakers, and dress shoes for men. Women should bring a pair of sandals, a pair of sneakers, and three to four pairs of dress shoes.