Points
A game goes 0 ("love"), 15, 30, 40, then game. If both players reach 40 it is deuce, and a player must win two points in a row: first "advantage", then the game.
Games and sets
A set is won by the first player to six games with a two-game lead, like 6-4. At 5-5 you need 7-5.
Tie-breaks
At 6-6 most sets go to a tie-break: points are counted 1, 2, 3, and the first to seven with a two-point lead wins the set 7-6. The serve changes after the first point, then every two points.
Matches
Most tournaments play best of three sets; men's Grand Slam singles play best of five.