The area in front of the goal is called the goal crease. It's where the goalie stands and guards the goal from opposing players making shots on goal. Players must be careful not to interfere with the goalkeeper in the crease, or they will be called for goalkeeper interference.
The goal lines are the lines that intersect the goal cages (red in color, but don't confuse with the center red line). The puck must completely pass the goal line within the goal cage to count as a score.
The goalie can only play the puck in the goalie trapezoid and in front of the goal line, as long as he doesn't cross the center red line. He is not allowed to play the puck behind the net outside of the goalie trapezoid.
For any goalie that plays the puck outside of goalie trapezoid, a minor penalty will be called, for a delay of game that lasts two minutes. As long as a goalie keeps his skate in contact with the goal crease, no penalty will be given.