Hockey players either shoot left or right. A left-handed shot in hockey is a player who holds his left hand on the lower part of his stick and the right hand on the upper part. Left-handed shots typically play on the left side of the ice, although some positions lend themselves to players who shoot either way.
Left-winger
The left-winger is the forward responsible for the left side of the ice on offense. He will typically move down the left side of the ice and dig for the puck in the opposing team's left corner. He can pass the puck back from this position, to the left defenseman or the center if he's open in the slot. When the opposing team gains the puck, the left-winger will cover his right defenseman. When skating backwards, his left-hand side will face the boards -- but if he needs to turn to catch up to the play, his right-hand side will face the boards. The left-winger won't usually play in the corners in his own end, but will stick to the right point -- just inside the blue line.
Left Defenseman
The left defenseman is responsible for stopping the right-winger on the opposing team. In his own end he plays on what is referred to as the right side -- from the perspective of the team on offense -- and he will fight for pucks in the right-hand corner. When on offense, the left defenseman positions himself on the left point in the opposing team's end -- just inside the blue line. The left-winger can drop the puck back to him from this position so he can shoot the puck, or cycle it through to the right defenseman.
Center
A center can be either left or right-handed. A left-handed center must be comfortable playing on both sides of the ice. On offense, he will typically play through the middle of the ice. As he approaches the goal with the puck, he can go to either side, but if he chooses the left side it leaves the puck more exposed and prone to being poke-checked. On the defensive side, the center will usually play up the middle, but must be comfortable in either corner.
Goalies
Like centers, goalies can be left or right-shooting. A left-shooting goaltender will wear a blocker on his right hand and a trapper on his left hand. The blocker is used to simply deflect shots, using the goaltender's weaker, right hand. The trapper is similar to a catcher's mitt in baseball, but unlike baseball, it is worn on the stronger hand. This allows a left-handed goalie to have greater control with his trapper hand than with his blocker.