Even though they live in the ocean all of the time, dolphins are mammals, not fish.
Like every mammal, dolphins are warm blooded. Unlike fish, who breathe through gills, dolphins breathe air using lungs. Dolphins must make frequent trips to the surface of the water to catch a breath. The blowhole on top of a dolphin's head acts as a "nose," making it easy for the dolphin to surface for air.
Other characteristics of dolphins that make them mammals rather than fish are that they give birth to live young rather than laying eggs and they feed their young with milk. Also, like all mammals, dolphins even have a tiny amount of hair, right around the blowhole, which is a little different than the scales of a fish.
Whales and porpoises are also mammals. There are 75 species of dolphins, whales, and porpoises living in the ocean. They are the only mammals, other than manatees, that spend their entire lives in the water.