You hit the shuttle up and which every way the shuttle head is facing that person serves first. In mixed (when a girl + boy play together) the girl always has to serve first. The first service is always made from the right hand side of the court.
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Any one player tosses the shuttle and a rally is held, the winner of the rally decides if he wants to serve or a court.
Generally, you would either decide between the 2 parties, or hit the shuttlecock upwards then whichever way it lies would receive the starting serve.