It is believed, that about 55 million years ago, a mammal which lived on land moved into the water, maybe looking for food. Over time, these animals became adjusted to living underwater, and slowly evolved into dolphins.
Dolphin ancestor
The land mammals learnt to feed on small fish in shallow waters, they began to spend an increasing amount of time foraging for food in swamps, estuaries and the ocean. They progressively adapted to a more aquatic way of life and passed through an amphibious stage before becoming fully aquatic about 40 million years ago. During this transition between land and ocean, these primitive dolphins resembled the behavior of today's seals, feeding in the sea and coming ashore to breed and to raise their young. Once these animals started living entirely within the ocean, it took millions of years for what is known as true cetacea to develop. It is believed that the Delphie group, from which today's dolphins arose, began appearing approximately 25 million years ago.
Bibliography:
http://www.tangalooma.com/dolphinweb/schoolprojects/
Gunzi, C. My Best Book of Whales and Dolphins. Kingfisher, 2001.