There are four species of puffins. Here I shall detail only the most important in depth, but most comments hold true for all four species.
Atlantic Puffin: Fratercula arctica
It is almost impossible to confuse a puffin with any other sort of bird. The Atlantic Puffin is perhaps a foot in length at the most, with a wingspan of twice that. Puffins have a white chest, a black back and a white face. They also have orange legs, and throughout most of the year have a distinctive bill, coloured red, orange and blue. The bill is large and hooked, and has been compared to that of a parrot. During the winter, following the breeding season, the face darkens, and the bill loses its colouration. Moulting, which stops the puffin's ability to fly occurs in early spring.
Puffins can "fly" underwater much like penguins, with surprising ease and speed. This allows them to catch fish. They can also fly in the air, but do not take off or land very well. When on land puffins are able to travel about on foot. They maintain an upright posture, and often hop in a recognisable manner.
The Atlantic Puffin lives in the North Atlantic, in coastal regions, or on small islands. It tends to live where there are no ground based predators, and where the supply of food is relatively plentiful.
To hunt for food, mainly fish and crustaceans puffins dive underwater, and swim around. Puffins are surprisingly tolerant of low water temperatures. Unless they are bringing food back to young, the catch is swallowed while the puffin is still underwater. In between dives, while out to sea puffins usually bob on the surface of the water, much like ducks. A puffin may spend months away from land at a time.
Puffins establish burrows in which they live, and breed. Puffins appear mature after only one year, but they do not return to breed until four or five years after they leave the burrow. Average life expectancy is about 20 years. The worldwide populations of all species is thought to be around 20 million.
While breeding, puffins dig their burrows very close to each other, forming dense colonies. In these colonies, there appears to be a lot of communication, mostly in the form of low growling noises. Colonies appear to defend themselves from gull predation by the formation of a whirling shield of puffins above the colony.
The courtship behaviour of the puffin is most interesting. Males attempt to make themselves seem large and impressive, by puffing out their chests, and throwing their heads back. This usually occurs in the water. Males may fight over females, but serious injury does not occur. When a pair have decided upon each other, they may display the behaviour known as billing, in which they tap their bills against one another.