Different dolphin species eat different food. Some of them eat fish: mullet, herring, cod; some eat squids. The large dolphins could even eat seals or sea lions. In some conditions they could eat turtles as well.
They need large amounts of food. A dolphin will eat around 4-9% of this weight in fish, so a dolphin of around 200 kg will eat daily over 10kg of fish, but it depends a lot of the fish he finds. Some fish species are fat, as mackerel and herring. Some of them have low caloric value. In the last case, they will need to eat much more. Of course, sometimes they will eat only as much as they can hunt :).
One usual dolphin hunt method is corralling where fish is chased to shallow waters where they cannot escape or hitting the fishes with the tail to stun them (for big fishes).
Dolphins are really intelligent and sometimes use not usual methods to feed themselves. One of these methods is called herding: one dolphin surrounds a school of fish that jump to escape right in the dolphins’ mouth.
In this video you can see an example of how a group of dolphins hunt fishes that try to jump from the water (BBC live video on YouTube):