The physics involved in a slapshot is incredible. When the shooter begins their slapshot, they actually aim about a foot before the puck. The stick hits the ice, and as you can see from the photo on the left, the stick flexes a fair amount. When the energy built up by the flex in the stick can no longer be held back by the force of the head of the stick on the ice, the stick flies forward striking the puck with an incredible amount of force. The average NFL shooter is capable of hitting a slapshot anywhere from 90-100 miles per hour. Before regulations and maximum stick weight were instituted in the 60's, Bobby Hull's slapshot was clocked at 120 miles per hour!
Of course the slapshot is not the only style of shot in hockey. There are wrist shots and backhand shot also, but those are not quite as interesting from a physics standpoint.