The park is a 2.5 hour boat ride from Key West. The boat has a toilet, bar, and some snacks.
The park was initially discovered by Spanish explorer Ponce de León (accompanied Columbus on his second voyage) who called the island Tortugas because they found turtles (Spanish for turtles) on the island. They rounded up several of the shellbacks and took them on board for food. If you splash salt water on them periodically, they'll stay fresh for several weeks / months.
British sailors visited later and found there to be no fresh water available so they added Dry to the name. The US later spent the money to ship bricks, timber, food, and troops to the island in support of Fort Jefferson. The intent was to defend shipping interests between the port in New Orleans and the east.