The vector for angular momentum points perpendicular to the velocity and force vectors. It goes according to the right hand rule. This is just a simple way of remembering where the angular momentum vector is pointing. The moment of inertia depends on the mass of an object and also the distribution of that mass around the axis of rotation. So a skater can have a different moment of inertia based on whether their arms are extended or not.
Angular momentum is conserved when no outside torques act on an object.
As say, the moment of inertia decreases, the angular rotation has to increase to keep the same angular momentum. This is most evident when a figure skater spins. This is how those incredible spins skaters like Paul Wylie, Todd Eldridge and Kristi Yamaguchi are accomplished. Along with many long years of practice. Most of the spins done by world class figure skaters are edge turns, meaning they are spinning while remaining on an edge.