Unofficial rules of the game known to the masses as "four square" (or "box ball" in Brooklyn, NY or "quad city" in Rock Island, IL) are as follows:

Rule the first ("The Rule"): If the ball bounces into your square, and then nobody touches it, and then it touches the ground again, then you are out. This is the primary rule and the foundation of the game of four square.

Rule the second ("Owning"): If you touch the ball, and then it bounces into your square, you are out; you have "owned" it.

Rule the third ("Hitting it Out"): If you touch the ball, and then the ball bounces out, you are out; you have "hit it out."

Rule the fourth ("Doublehit"): If you touch the ball, and then before it touches anyone or anything else, you touch it again, you are out; you have "doublehit."

Rule the fifth ("Palming"): If you touch the ball for a duration offending the sensibilities of those playing, you are out; you have "palmed" it.

Rule the sixth ("Dribbling"): If you touch the ball, and then the ball bounces into an opponent's square, and then nobody else touches it, and then you touch it again, you are out; you have "dribbled."

Thus enumerated are the ways of getting out after the serve. After one person is out, the round is over. No one else becomes out until the next round. Each round, exactly one person becomes out.

 The four square court, including the boundaries of the squares

A four square court looks something like this:
 ---------
|    |    |
| 1  | 2  |
|    |    |
|----+----|
|    |    |
| 4  | 3  |
|    |    |
 ---------
(Except it is four squares, not four non-square rectangles.)

The outer lines are considered in, not out.
The line between squares 1 and 2 is considered part of square 1.
The line between squares 2 and 3 is considered part of square 2.
The line between squares 3 and 4 is considered part of square 3.
The line between squares 4 and 1 is considered part of square 4.
The central point is considered part of square 1.

 The serve
At the beginning of each round, the player in square 1 serves the ball. This means (s)he:
(i) stands behind square 1 from the vantage point of square 4 and behind square 1 from the vantage point of square 2,
(ii) drops the ball into square 1,
(iii) then hits the ball, with intention to serve.

As soon as the player in square 1 hits the ball with intention to serve, the ball is in play, and thus the six rules apply. To clarify, this means if the ball goes out of bounds or into square 1 on the serve, the player in square 1 is out for hitting it out or for owning, respectively.