There are two main kinds of golf competition using handicaps: stroke play and match play. In stroke play, the player with the fewest net strokes on the entire round wins. In match play, the player with the fewest net strokes on a given hole wins that hole.
First you must determine your course handicap -- this is a calculation that combines your handicap index from CDGA with the slope of the particular course you are playing. At a course that is easier than the norm (slope of 113), your handicap will be lower than your index, and visa versa. All pro shops should have tables for computing course handicaps; however, they can also look up their course handicap using the USGA Course Handicap Calculator.
In stroke play, each player will subtract the course handicap from her total score to record her handicap score for the round. In match play, players compare their handicaps, and the player with the higher handicap receives a stroke per hole up to the difference in handicap between her and her opponent. For example, if player A has a handicap of 30 and player B a handicap of 23, then player A receives a stroke (that is, a one-shot advantage) on each of the 7 hardest rated holes on the course. Course scorecards indicate the handicap ratings for each hole, with 1 being the hardest rated hole.