A fish swims by using the muscles of its powerful tail. The tail fin swishes from side to side. As it moves sideways, the tail also gives a backward push on the water. By pushing back against the water with its tail fin the fish moves itself forward.
Doesn't a fish ever paddle itself along with its other fins? Hardly ever. Most fish use the other fins for steering or balancing. Some use them as feelers when they hunt for food at night.
A fish called the shark-sucker has a fin like a suction cup. The fish sticks its cup onto a shark's body and hitchhikes along until the shark finds something to eat. Any morsels that fall from the shark's mouth are gobbled by the sucker.
The fins of a flying fish act like glider wings when it leaps out of the water and soars through the air.
Fishes must constantly be swimming in order to keep from sinking.