To keep track of individual dolphins, we identify them by their unique dorsal fin characteristics, such as shape and notches. Dolphins get notches in their fins from playing and fighting with each other, and from encounters with sharks, particularly tiger sharks.
Below is an example of the dorsal fins of two female dolphins, Bytfluke (left) and Joy (right). You can see that Bytfluke's dorsal fin has a very distinctive shape, making her easier to identify than Joy.
We keep a very detailed photo identification catalog of the dolphins and each time their dorsal fin changes, we get another picture. Sometimes, if the dorsal fin changes radically, we can still identify the dolphin by other body markings. In addition, they usually don't change their dolphin friends when their fin changes, so we can figure out who the 'mystery' dolphin is by seeing who his or her friends are. Experienced scientists studying dolphins recognize them instantly, the way we do when we see our human friends.