Please see my review about the Yankee Freedom III, the ferry that brings most visitors to the Dry Tortugas, for details about that–briefly, it's a good service and worth the money to get to this unusual location and historic landmark. You can also take your own boat or charter a seaplane.
First, expectations: This is not a cruise stop and not a tourist trap. It's a national park. The portion you're permitted to tour (if you come by ferry) is the ruin of a 19th century fort built on an island not much larger than itself, 70 miles west of Key West. It takes 2.5+ hours to get there. It is hot. There is no phone or internet service. There's not much shade on the beaches. There's no shopping except a little gift shop, and no food, water or restroom facilities except on the ferry (which also serves breakfast and lunch, and which you can return to).
But if you like architecture and history, being outside, swimming, snorkeling, birding, photography, great views and/or strange, beautiful out-of-the-way places, you'll probably be very happy with your visit. For the more adventurous, primitive camping is available.
Ft. Jefferson is an immense, mostly empty 6-sided building with an open center. The vaults, brickwork, spiral staircases and the moat (yes, an island with a moat) are impressive. You can climb up to the roof/parapet, where you can see the cast iron harbor light and cannons, and get an amazing view of the entire island and the ones nearby. If you don't take the ferry's tour, you can explore on your own using the provided guidebook and signs. You can also walk the path on the moat wall.
Snorkeling is allowed in several locations. We felt the best one was the south coal dock ruins, near the ferry dock. Above water, terns, seagulls and pelicans perch on pilings and look down on you from only several feet away. Below, what's left of the structure is the foundation of a sort of artificial reef, crusted with coral and marine plants. The area was packed with fish. Snorkeling along the outer moat wall (you can't swim in the moat itself) is also interesting, because you can observe the activities of baby/juvenile fish and cleaning stations. On a calm, sunny day, the water in the moat and around the fort are beautiful shades of turquoise and blue. The ferry staff can equip you with snorkeling gear if you don't have it.
Be sure to use sunscreen, wear a hat and sunglasses, and bring a pre-filled water bottle (at least a liter/quart) to take with you when you leave the ferry–you can also bring small coolers with you. In addition to bottled water for sale, there is a water jug on the ferry, but be polite–it's meant for everyone to share with the meals. Wear good shoes or sport sandals. There are some changing rooms at the dock.