This is one of the common applications of the law of conservation of momentum. The initial momentum is zero, and since, there is no external unbalanced force, the final momentum remains zero as well. Thus, the skater will recoil in the opposite direction so as to make the total momentum of the system(ball + skater) zero. Nicely explained in the video:
http://in.youtube.com/watch?v=vPkkCOlGND4
Elcues Team

