A skater spins in the counterclockwise direction, as seen from above. In what direction does the vector representing the angular momentum of the skater point.

To find the direction of the angular momentum we use the right hand rule in the same way we used it for angular velocity. Thus, if we look down on the skater and curl our fingers around in the counter clockwise direction, our thumb points towards us. Thus, the angular momentum of the skater is pointing upwards.