The angular momentum, L, of a point mass is defined as the cross product of the object's linear momentum, p, and its moment arm with respect to a fixed pivot point, r.
L = r x p
Remember that since L is a vector cross product, all three of these vectors must be mutually perpendicular to each other. That is, L, r and p must be in three separate planes. L is measured in kg m^{2}/sec.
Using an analogy to torque we will once again use the right hand rule (RHR): r is your fingers, palm is p = mv, thumb is L.
For example, suppose a mass is falling while attached to the end of string that is unwinding from a pulley.

the momentum of the mass is in the y direction (palm),

the moment arm away from the fixed pivot towards the line of action of the falling mass' momentum is in the x direction (fingers), then

the angular momentum is in the +z direction (thumb).
Let's look at an example of how we can use a determinant to calculate the angular momentum of the falling mass in the previous diagram with respect to the pulley's axis of rotation. 