Shelter
A tent plays an essential role in your comfort while camping on the island. It will provide shelter from the sun, wind and insects and give you privacy as well. How large a tent you bring depends on the size of your party and your preference, but remember that the park requires freestanding tents---you cannot tie off or guy tents, hammocks or canopies from the trees in the campground.
Bedding
A light sleeping bag or blanket will probably prove sufficient for your needs given the warm climate. Bring a sleeping pad or inflatable mattress for extra cushioning if you don't want to "rough it" too badly.
Food and Water
The island has no facilities for purchasing food or drink on the island, and the campground has no fresh water available. Pack sufficient food for your entire stay, and bring enough water to meet your needs---a gallon of water per person, per day. Plan out your menu ahead of time to ensure that you have enough food for your stay. If you plan on bringing perishable foods (or want cold beverages), bring a cooler with ice.
Rats liveon the Dry Tortugas---an inevitable byproduct of man's habitation of the island. Pack all food in hard containers, and don't leave out scraps.
Cooking Gear
Campsites at the Dry Tortugas have a grill, so you can cook your food that way. However, wood fires are not permitted and you must pack in your own charcoal. For an easier option, bring a gas camping stove if you plan on doing any cooking.
Personal Items
Remember that you'll inhabit a tropical island during your stay, so don't forget your sunscreen and a hat. Pack any essential toiletries and medications, and remember that the island has no showers. Bring baby wipes for personal hygiene needs and for freshening up.
Foul weather can move in rapidly on the island, prepare yourself with foul weather gear.