How does golf match play scoring work?

In match play, the score (that is, number of shots, or "strokes") is considered seperately for each hole, rather than a total for 18 or more holes, as in stroke ("regular") play. Then, the player who wins (has the lower score for) more holes wins the match. Think of it as the World Series or NBA Finals, with each hole being one "game" in an 18-game series. One major difference here is that players can tie a hole ("halve" the hole being the proper term), in which case the hole counts as zero wins for both players.

When the match starts, the players are tied at zero, or "all square". When a player wins a hole, he/she is "one up"; likewise, his/her opponent is "one down". If a player who is 1up wins the next hole, he/she is "two up", with his/her opponent being "two down", and so on. If the 1up player should lose the next hole, the players are all square again. If a 2up player should lose a hole, he/she is 1up again, and so on. If the players halve, or tie, a hole, the score remains the same. If at any time the amount of holes a player is "up" exceeds the remaining number of holes, the match is immediately called, and that player wins. Say a player is 3up after hole 16. This player wins being 3 up with 2 holes remaining, denoted "3 and 2". If the player wins with a final score of 1up or 2up, that means the game went the full 18 holes, otherwise it would have been denoted in the "x and y" fashion. If a player's lead is equal to the remaining number of holes, the match is said to be "dormie", and the down player must win every remaining hole to force extra holes. Any hole halved, or won by the up player, will cause the up player's victory. If the players are all square after 18 holes, they play additional holes until someone wins a hole. When this happens, the score is usually donated as the hole the match was won on; one would then know that the match was square after 18, and the player won on the denoted hole. Scoring examples:

Al and Bob are starting the 12th hole. Al is 3 up, so Bob is 3 down. This means Al has won 3 more holes than Bob. This could be because Al has won 7 holes and Bob won 4, because Al has won 3 and the rest we halved, or any combination in between. Actual number of holes won is not tallied.

Al is 3 up teeing up on the 15th hole. Al wins the hole, and thus the match, 4 and 3. (Al is 4 up, and only 3 holes remain. If Bob wins every hole, he'll still be behind)

The boxscore rolling along the bottom of SportsCenter says Chuck defeated David, 21st hole. This means Chuck and David were all square after 18 holes, so they played extra holes. They halved two holes (19 and 20), and Chuck won the 21st hole, and thus the match.

Also worthy of note is that in addition to ending a match when victory is unattainable for one player, a hole will be ended when victory for that hole is clinched, as well. For example, Ed and Frank each reach the green in 2 shots on a par 5. Ed makes his eagle putt, Frank missed his. Frank would then just pick up his ball, and the match would proceed to the next hole. The number of strokes Frank would have needed to finish the hole is inconsequential.