Table tennis serving rules have changed over the years.  Under the current ITTF rules, the player to serve first is chosen at random, with the winner of the random draw able to choose to serve first or receive first.  Sometimes in casual games, the first serve is chosen by volley, where a "practice" rally is played to determine who serves first.

The player who is serving changes after a certain number of points are scored.  Under the current ITTF rules, in an 11 point game, the service changes every 2 points.  In the past, when games were played up to 21 points, the service changed every 5 points.

Here is an example of how this works.

 - Player A serves first to Player B.  They each get one point, and the score is 1-1.  The total score is now 2, so it is Player B's turn to serve.
 - Player B gets the next 2 points, and the score is 1-3.  The total score is now 4, and the serve switches back to Player A.
 - Player A continues serving until the total score is 6.

In an 11 point game, the game must be won by a 2-point lead.  If both players score 10 points, the service switches after every point until the game is over.

The current ITTF rules for order of serving are found in the [ITTF Handbook](http://www.ittf.com/ittf_handbook/ittf_hb.html), section 2.13.