The foursquare player location in the highest numbered square begins the game by serving the ball from the outside corner of the square. The ball must bounce once in the servers own square before entering another players square. Players must let the ball bounce once in their own square, and then return the ball in the same method as the server. Balls are similar to kickballs and dodgeballs, being light rubber and with good bounce. The play must only use their hands to hit, serve, or return the ball. Carrying or holding or catching the ball are all penalties and forfeits.

Once the ball touches the play surface in another players square, that player must continue by hitting it into any other square. The ball continues to be hit back and forth between squares until a player makes a forfeit or penalty, and gets eliminated by leaving the square.

The rest of players move up to their next highest squares number, and another (or the recently eliminated) player joins the game in the lowest square (one). If there are more than four players foor a square, the eliminated players just wait in line for their turn to re-enter the game.

Hold the ends of the ropes tightly, shoulder width apart, about waist high, but do not wrap the rope around your hands. Rope turners should always start turning the rope closest to the jumper first, to enable the jumper to enter the ropes easier. Turn the ropes inward in small circles by turning the right forearm counter clockwise and left forearm clockwise like an eggbeater, while avoiding crossing the midline of your body with your hands as they rotate the jump ropes. You can count one-two’s to help establish a rhythm for both turners, and jumper.

The person jumping in, aka the jumper, stands next to one of the jumprope turners and faces the other rope turner. The jumper-in’s legs should be in position with their leg closest to the rope turner facing away from the rope and the other leg closer to the rope. Jumping In starts when the jumper-in enters the ropes as the rope closest to the jumper passes their eye level. Take one large step and a single jump, and leap into the middle of the rope with the leg closest to the rope turner hitting the floor first. The jumper begins jumping using a two-foot basic marching jump. If your just learning, use the single bounce jump in, and then slowly work your way up to two ropes.

UPDATE: a great recent story on NPR highlights the increasing use of physical jumprope and double dutch games in particular in nationwide schools as tournament play:

Location: In Basketball court, or something similar to it.
There are 2 teams with equal number of players. One of the players from both sides needs to be the TARGET. The target needs to stand on the far side line, he can’t move out of the line but he can move side to side, not stepping out of the free throw line.
The players are to run and try to hit the TARGET with a dodgeball or soft kickball to score 1 point, once 1 point is scored, they need to change their target.
At the start, players go to the middle of the court and do something, like flipping a coin, to choose the starting team. Once started, players need to pass the ball.
You can’t move with the ball in your hand, but you are allowed to make false steps or move one foot, but standing at the same spot. When have the ball, you can’t dribble or dodge around, so you need to pass the ball to someone.

When you have the ball, pass. When you don’t, look for pass.
Now the target rules and fouls:
The players can’t cross the freethrow line when they shoot. The players CAN stand inside the freethrow line, they can go anywhere. But if a player has the ball inside the freethrow line, or someone catches the pass INSIDE the freethrow line, it is a foul. When a player pushes, kicks, etc. are also all fouls.
Referees arent necessary in this game, unless the players wish.
When a player from team 1 commits a foul, then team 2 needs to go to their free throw line, stand in the line and shoot at the target. The target can move side to side, can jump dodge etc.