Answer:
A crossover requires lateral quickness and deception. The goal is to have your opponent think you are going one way, and just when he begins to go that way, you quickly burst towards the opposite direction, leaving your opponent watching.
The basic way to do a crossover is to have your momentum slightly going left, enough to where your defender is on your left side or moving left. You will then suddenly change directions, pushing off of your left foot to go right, leaving your opponent in the dust.
View the related links below for some fantastic crossovers in the NBA.