the basics

Each game is played to 21 points, with players scoring a point whenever they win a rally regardless of whether they served [7] (this differs from the old system where players could only win a point on their serve and each game was played to 15 points). A match is the best of three games.
At the start of the rally, the server and receiver stand in diagonally opposite service courts (see court dimensions). The server hits the shuttlecock so that it would land in the receiver's service court. This is similar to tennis, except that a badminton serve must be hit below waist height and with the racquet shaft pointing downwards, the shuttlecock is not allowed to bounce and in badminton, the players stand inside their service courts unlike tennis.
When the serving side loses a rally, the serve immediately passes to their opponent(s) (this differs from the old system where sometimes the serve passes to the doubles partner for what is known as a "second serve").
In singles, the server stands in her/his right service court when her/his score is even, and in her/his left service court when her/his score is odd.
In doubles, if the serving side wins a rally, the same player continues to serve, but s/he changes service courts so that s/he serves to a different opponent each time. If the opponents win the rally and their new score is even, the player in the right service court serves; if odd, the player in the left service court serves. The players' service courts are determined by their positions at the start of the previous rally, not by where they were standing at the end of the rally. A consequence of this system is that, each time a side regains the service, the server will be the player who did not serve last time.