Okay... done teaching now...
To simplify calculations in a 2 dimensional system, find the x and y components of each object in the system (if an object is at rest, the x and y components of momentum = 0)
The find the sum of the x-components of momentum, and the sum of the y components of momentum. This is the net momentum in each direction and will remain the same (provided you don't add any forces).
Example that doesn't look like momentum is conserved. object moving to the right and an object moving to the left, but not perfectly lined up with each other. Initial net momentum in the y direction = 0. After they strike each other with a glancing blow, both of them travel off at some angle. A portion of the momentum of each is in the y direction. If you add the y components of each together, they will cancel out to give you a net momentum in the y direction of 0. (momentum is a vector; so since they're in opposite directions, define one direction as positive and one direction as negative)