The two most common infractions you will see called in hockey are offsides, icing, and offside pass (or sometimes called a two line pass.) Here are their descriptions, along with a graphical representation of what happens on the ice during these infractions. In all cases, the team with the puck would be trying to score on the goal at the right of your screen.

A team is offside when any member of the attacking team precedes the puck carrier over the defending team's blue line. The position of the player's skates and not that of his stick is the determining factor. If both skates are over the blue line before the puck, the player is offside. If he only has one skate over the blue line and one on the blue line, he is onside. In the example (left) notice how player B crosses the blue line before player A who has the puck does.

Icing is not permitted when teams are at even strength. Icing occurs when a player on his team's side of the red (center) line shoots the puck all the way down the ice, it crosses the red goal line at any point other than the goal itself and is first touched by a defending player. Play is then stopped and the puck is returned to the other end of the ice for a face-off. Icing is not called if the goalie plays the puck by leaving his net, if the puck cuts across part of the goal crease, when a defending player, in the judgement of the linesman, could have played the puck before it crossed the red goal line, when an attacking player who was onside when the puck was shot down the ice manages to touch it first, or when the attacking team is playing short-handed because of a penalty. In the example (left) notice how player A from the blue team manages to get to the puck before Player A from the green team, the one who shot the puck down the ice, can get to it.