Each player or pair takes position either side of a net, on a rectangular court marked on the floor. The object of the game is to hit a shuttlecock (more colloquially, "bird" or "birdie") using a racquet, over the net such that the opposing player or pair cannot hit it back before it hits the floor and the shuttlecock does not land outside the marked court. For every time this is achieved, the player or pair scores one point, if they were serving. If the opposing team was serving, there is a change of server. The first player or pair to reach 15 points (11 points for women) wins a game.
A badminton match can be made up of any odd number of games (usually 3). The winner of the match is the first to win more than half the number of games (e.g. the first to win 3 games in a 5 game match).
In both singles and doubles, there is a change of service when the server loses a point. In doubles, the first team to serve has one player serve. All other times, both players on the team serve in succession.
One of the best links with more information (rules, equipment etc.) is http://www.intbadfed.org/ - International Badminton Federation.
The following was originally from the 1911 Encyclopedia Britannica. As such, it may not yet be properly adapted to Wikipedia (obsolete, typos, no accidental links, etc.). It is included as a stub of sorts to inspire you to fix these problems and modify it:
Badminton, or Great Badminton, a village in the southern parliamentary division of Gloucestershire, England, 100 m. W. of London by the Great Western railway (direct line to south Wales). Here is Badminton House, the seat of the dukes of Beaufort, standing in a park some 10 m. in circumference. The manor of Badminton was acquired in 1608 from Nicolas Boteler (to whose family it had belonged for several centuries) by Thomas, Viscount Somerset (d. 1650 or 1651), third son of Edward, 4th earl of Worcester, and was given by his daughter and heiress Elizabeth to Henry Somerset, 3rd marquess of Worcesterand 1st duke of Beaufort (1629—1699), who built the present mansion (1682) oh the site of the old manor house. It is a stone building in Palladian style, and contains a number of splendid paintings and much fine wood-carving. The parish church of St. Michael stands close to it. Thisis a Grecian building (1785), with a richly ornamented ceiling and inlaid altarpavement; it also contains much fine sculpture in the memorials to former dukes, and is the burial-place of Field Marshal Lord Raglan, who was the youngest son of the 5th duke of Beaufort. Raglan Castle, near Monmouth, now a beautiful ruin, was the seat of the earls and the 1st marquess of Worcester, until it was besieged by the Parliamentarians in 1646, and after its capitulation was dismantled.
Badminton, a game played with rackets and shuttlecotks, its name being taken from the duke of Beaufort's seat in Gloucestershire. The game appears to have been first played in England about 1873, but before that time it was played in India, where it is still very popular. The Badminton Association in England was founded in 1895, and its laws were framed from a code of rules drawn up in 1887 for the Bath Badminton Club and based on the original Poona (1876) rules.
In England the game is almost always played in a covered court. The All England championships for gentlemen's doubles, ladies' doubles, and mixed doubles were instituted in 1899, and for gentlemen’s singles and ladies’ singles in i9oo; and the first championship between England and Ireland was played in 1904. Badminton may be played by daylight or by artificial light, either with two players on each side (the four-handed or double game) or with one player on each side (the two-handed or single game). The game consists entirely of volleying and is extremely fast, a single at Badminton being admitted to require more staying power than a single at lawn tennis. There is much scope for judgment and skill, e.g. in "dropping" (hitting the shuttle).
In the two-handed game, the width of the 2'6" Back Boosdury Line court is reduced to 17 ft. and the Long Service Line the long service lines are dispensed with, the back boundary lines being used as the long service lines, and the lines dividing the half courts being produced to meet the back Short Service Line boundary lines. The net posts 6' 6" are placed either on the side boundary lines or at any distance not exceeding 2 ft. outside 66 the said lines; thus in the four-handed game, the distance between the post is from 20 to 24 ft., and in the two-handed game, from 17 to 21 ft. NB With the exception of the net line, the dotted lines on the court apply only to the court for the two-handed game. gently just over the net) and in "smashing" (hitting the shuttle with a hard downward stroke). The measurements of the court are shown on the accompanying plan.
The Badminton hall should be not less than 18 ft. high. Along the net line is stretched a net 30 in. deep, from 17 to 24 ft. long according to the position of the posts, and edged on the top with white tape 3 in. wide. The top of the net should be 5 ft. from the ground at the centre and 5 ft. 1 in. at the posts. The shuttlecock (or shuttle) has 16 feathers from 21/2 to 23/4 in. long, and weighs from 73 to 85 grains. The racket (which is of no specified size, shape or weight) is strung with strong fine gut and weighs as a rule about 6 oz.
The game is for 15 or, rarely, for 21 aces, except in ladies' singles, when it is for xi aces; and a rubber is the best of three games. Games of 21 aces are played only and always in matches decided by a single game, and generally in handicap contests. The right to choose ends or to serve first in the first game of the rubber is decided by tossing. lithe side which wins the toss chooses first service, the other side chooses ends, and vice versa; but the side which wins the toss may call upon the other side to make first choice. The sides change ends at the beginning of the second game, and again at the beginning of the third game, if a third game is necessary. In the third game the sides change ends when the side which is leading reaches 8 in a game of 15 aces, and 6 in a game of xx aces, or, in handicap games, when the score of either side reaches half the number of aces required to win the game. In matches of one game (21 aces) the sides change ends when th’e side which is leading has scored ii aces. The side winning a game serves first in the next game, and, in the four-handed game, either player on the side that has won the last game may take first service in the next game.
In a game of 15 aces, when the score is "13 all" the side which first reaches 13 has the option of "setting" the game to 5, and when the score is "14 all" the side which first reaches 14 has the option of "setting" the game to 3, i.e. the side which first scores 5 or 3 aces, according as the game has been "set" at "13 all" or "14 all," wins. In ladies’ singles, when the score is "9 all" the side first reaching 9 may "set" the game to 5, and when the score is "10 all" the side which first reaches 1o may “set” the game to 3. In games of 21 aces, the game may be "set" to 5 at "19 all" and to 3 at "20 all." There is no "setting” in handicap games.
In the four-handed game, the player who serves first stands in his right-hand half court and serves to the player who is standing in the opposite right-hand half court, the other players meanwhile standing anywhere on their side of the net. As soon as the shuttle is hit by the server’s racket, all the players may stand anywhere on their side of the net. If the player served to returns the shuttle, i.e. hits it into any part of his opponents’ court before it touches the ground, it has to be returned by one of the "in" (serving) side, and then by one of the "out" (non-serving) side, and so on, until a "fault" is made or the shuttle ceases to be "in play." (The shuttle is "in play" from the time it is struck by the server's racket until it touches the ground, or touches the net without going over, or until a "fault" is made.) If the "in" side makes a "fault," the server loses his "hand" (serve), and the player served to becomes the server; but no score accrues. If the "out" side makes a "fault," the "in" side scores an ace, and the players on the "in" side change half courts, the server then serving from his left half court to the player in the opposite left half court, who has not yet been served to. Only the player served to may take the service, and only the "in" side can score an ace. The first service in each innings is made from the righthand half court. The side that starts a game has only one "hand" in its first innings; in every subsequent innings each player on each side has a "hand," the partners serving consecutively. While a side remains "in," service is made alternately from each half court into the half court diagonally opposite, the change of half courts taking place whenever an ace is scored, If, in play, the shuttle strikes the net but still goes over, the stroke is good; but if this happens in service and the service is otherwise good, it is a "let," i.e. the stroke does not count, and the server must serve again, even if the shuttle has been struck by the player served to, in which case it is assumed that the shuttle would have fallen into the proper half court. It is a "let," too, if the server, in attempting to serve, misses the shuttle altogether. It is a good stroke, in service or in play, if the shuttle falls on a line, or, in play, if it is followed over the net with the striker’s racket, or passes outside either of the net posts and then drops inside any of the boundary lines of the opposite court. Mutatis mutandis, the above remarks apply to the two-handed game, the main points of difference being that, in the two-handed game, both sides change half courts after each ace is scored and the same player takes consecutive serves, whereas in the double game only the servl~ig side changes half courts at an added ace and a player may not take two consecutive serves in the same game.
It is a "fault":
For full information on the laws of the game the reader is referred to the Laws of Badminton and the Rules of the Badminton Association, published annually (London). See also an article by S. M. Massey in the Badminton Magazine (February 1907), reprinted in a slightly revised form in the Badminton Gazette (November 1907). Until October 1907 Lawn Tennis and Badminton was the official organ of the Badminton Association; in November 1907 the Badminton Gazette became the official organ.