The only difference between badminton rules for doubles and badminton rules for singles is the in/out boundaries for a badminton service and the in/out boundaries after the service has been delivered.
The correct area to stand in while delivering a badminton service is illustrated below:

The picture above shows the area that is considered INSIDE for a badminton serve in a badminton doubles game.

The picture above shows the area that is considered INSIDE during a badminton game after the service has been delivered in a badminton doubles game.
The fouls for a badminton doubles game are similar to badminton for singles. See the possible badminton fouls you could commit during a casual badminton game.