The basic scoring for bridge is simple. Here is a chart of how many points each level of the bidding is worth.

Points for Contracts
No-trump(first trick)4080160
No-trump(each additional trick)3060120
All of these points are below the line, which means they count towards game. A partnership makes game when they get 100 points below the line. So, under normal circumstances (in an undoubled contract), a bid of 5 clubs, 5 diamonds, 4 hearts, 4 spades, or 3 notrump is a game bid. Since clubs and diamonds are worth less than the other suits, they are called minor suits. Since hearts and spades are worth more, they are called major suits. After each game, a new line is started on the scoresheet - points from one game do not count towards the next game for either partnership.
Also, you also get points if you make more tricks than your contract. For example, if you bid 2 hearts, and took 10 tricks, you made 2 overtricks. These points are all above the line, which means they do not count towards game. The point values for overtricks are listed in this table.
Points for Overtricks
NonvulnerableNormal trick value100200
VulnerableNormal trick value200400

However, if your side does not make your contract, the opponents score points for the tricks that you did not make, but should have made, called undertricks. For example, if you bid 5 clubs, and only take 7 tricks, you made 3 undertricks. The point values for undertricks are scored above the line on the opponent's side, and are listed in this table.
Points for Undertricks
Type of ContractVulnerability of DeclarerFirst UndertrickEach Additional Undertrick

If your partnership makes a doubled or redoubled contract, you also receive 50 points scored above the line.
In addition to these bonuses, you can also score points for having honors points. Here is the table. Notice that any player may score these points.
Four trump honors (including 10) in one hand100
All five trump honors in one hand150
All four aces in one hand in notrump150

There are special bonuses for slams. These only apply if the slam is bid and made. These are listed in the table below. These bonuses are above the line.
Slam Bonuses
VulnerabilitySmall slamGrand slam

At the end of the rubber, your side gets points if you win two games before the other side does. If your partnership wins 2 games to none, then your side gets a 700 point bonus scored above the line. If your partnership wins 2 games to 1, your side gets a 500 point bonus scored above the line. At the end of the rubber, all the points are added up (above and below the line) on both sides, and the side who has the most points wins. Note that it is possible to win the rubber without winning two games (you could have more bonuses than the other side).