Tennis scoring is strange, and the strangeness is the point. It is not a running total. It is a nested series of short contests, each of which resets, which means a match is not won by whoever wins the most points. Understanding that structure is not trivia — it changes which points you should be willing to take risks on.
The four levels
Points
Within a game, points are counted 0 ("love"), 15, 30, 40, game. The numbers are historical convention and carry no arithmetic meaning; you can read them as first, second, third and fourth point without losing anything. The server's score is always called first, so "thirty–fifteen" means the server has two points and the receiver one.
If both players reach 40, the score is deuce. From deuce, a player must win two consecutive points to take the game: the first of them is called advantage, and losing the next returns the score to deuce. There is no limit to how many times this can repeat. Some recreational and doubles formats replace this with a deciding point at deuce — a single sudden-death point, with the receiving side choosing which court it is played to. Agree which you are using before you start; disputes about it are the single most common scoring argument in club tennis.
Games
Service alternates game by game. Within a game, the server serves every point, starting from the right (deuce) court and alternating sides after each point. Because holding serve is the expected outcome at most standards above beginner, the entire tactical shape of a set is built around the few games where that expectation is under threat.
Sets
A set goes to the first player to win six games with a margin of at least two. At 6–5 the leader may serve out at 7–5; at 6–6 a tiebreak is played in nearly all modern formats. Players change ends after the first game of a set and thereafter after every odd-numbered game, which exists to share out wind and sun rather than for the rest.
Tiebreaks
A standard tiebreak is played to seven points, margin of two. The serving order is the part people get wrong: the player whose turn it is to serve serves one point from the deuce court, then service passes to the opponent for two points, and thereafter in twos, alternating. Ends change after every six points. Whoever served first in the tiebreak receives first in the following set.
Many formats now replace a deciding third set with a match tiebreak to ten points, margin of two, using the same serving pattern. This is a genuinely different contest and rewards a different mentality — see the tactics note at the end of this page.
The rules club players most often get wrong
The let
A serve that touches the net cord and still lands in the correct service box is a let, and that serve is replayed — a first-serve let is replayed as a first serve. A let is not a fault, and there is no limit on consecutive lets. If the ball touches the net and lands outside the box, it is simply a fault. Note that some formats have adopted no-let serving, in which a net-cord serve landing in is played; again, agree in advance.
Touching the net
If you or anything you are wearing or carrying touches the net, net posts or your opponent's side of the court while the ball is in play, you lose the point — even if the point was already effectively over. Once the point has genuinely finished, it does not matter. The common error is a player who volleys a winner and then falls into the net before the ball has bounced twice.
Reaching over the net
You may not reach over the net to play a ball — with one exception. If a ball bounces on your side and the spin or wind carries it back over the net to your opponent's side, you may reach over to play it, provided you do not touch the net. This happens perhaps twice a season and causes an argument every time.
The double bounce and the frame
The ball must be struck before its second bounce. A ball that hits the frame and goes in is entirely legal; there is no such thing as an illegal mishit. A ball may be struck only once per shot, but an unintentional double contact within a single continuous swing is permitted.
Calling lines
In matches without officials, each player calls the lines on their own side, and the convention is unambiguous: if you are not certain the ball was out, it was in. A ball touching any part of the line is in. Calls should be immediate and audible. The full text of these rules, including the officiating procedures, is published by the ITF in the Rules of Tennis, and it is short enough to read in one sitting.
What the structure means tactically
Because the score resets at every level, points are not equally valuable. A point at 40–0 is worth far less than a point at 30–30, because the second one is close to deciding a game and the first one is not. The practical consequence is that the right amount of risk varies within a game: the cheap moment to attempt a low-percentage shot is when you are ahead in a game you are likely to win anyway, and the expensive moment is at deuce.
The same logic scales up. In a match tiebreak to ten, there is no room to lose a stretch of points and recover through a long set, so the shot selection that wins a first set on a slow court can lose a match tiebreak outright. Knowing which format you are in before the first point is a real tactical advantage, and it costs nothing.