Only 1's count in the first round, 2's in the second, etc. After all twenty rounds have been completed whoever has the highest score wins. The second way to win is to hit a Shanghai (one dart in the single, one dart in the double and one dart in the triple). If you hit a Shanghai, the game is immediatiately over and you win regardless of the player scores. If you hit a double or a triple with the first dart, always try for the Shanghai. If you miss it, you will still have a decent score.
There are a few variations to Shanghai that make it tougher to win. You can increase the skill level by making a Shanghai only count if the last dart is a double or triple, not a single. You can also make numbers on the board a must hit number. For example, if you were playing "must hit 7's" if a player doesn't hit at least one 7 he loses half his point total. These add-ons can also be used as a handicap for highly skilled players.