Yeah, as willy_c mentioned you assign each group of cards a value.. generally its 2 to 6 a +1, 7-9 a zero, and a card worth 10/ACE a value of -1.
The strategy is then to wait until the count is high, so that it is statistically more likely that a high card will come out (as if the count is high, then more lower cards have been played). And since the dealer is forced to hit on 17 or less, it is more likely that they will bust because its more probably that a higher valued card will fall, thus going over 21 (as you are able to see their revelead card)... Obviously its more complicated then that, but I beleive that is the general theory behind card counting. There are more variants on the way you assign values etc.
As has been mentioned, it relies on knowing how many cards are in the shoe, and that cards arn't replaced once they have been dealt etc.
I thought the movie was ok, a bit too... 'Hollywood'.
