Outline of the Game
1. The sides are Blue and Black versus Red and Yellow (or Green and Brown versus Pink and White). Doubles or Singles can be played: in Singles the player plays both balls of his side in alternative turns. In Doubles each player plays one ball only.
2. Play progresses in strict colour order: Blue, Red, Black, Yellow (the order of colours on the peg), then back to Blue again. If second colour balls are being used, then the sequence is Green, Pink, Brown, White.
3. Each turn consists of one stroke only. There are never any extra strokes for running hoops or hitting other balls.
4. A full-sized court measures 35 by 28 yards, and is laid out with six hoops and a centre peg. The order and direction in which hoops are scored is shown in the diagram.
5. The game starts by playing the balls in order from a position within one yard of corner 4 (the bottom right corner, as shown in the diagram).
6. All players try in successive turns to run (i.e. pass through) Hoop 1. As soon as any player on either side completes the running of Hoop 1, then he scores that hoop point for his side, and all players move on to Hoop 2, and so on around the court. Thus each hoop is scored only once, for one side or the other. The side to have scored the hoop may mark this by putting a coloured clips on the crown of the hoop.
7. The peg plays no part in Golf Croquet, other than as an obstacle and a reminder of colour order.
8. The game ends as soon as one side has scored seven points.
The Turn
9. A turn consists of a single stroke. A stroke is played when the striker hits any ball with his mallet and causes it to move, or commits a fault.
10. When all balls have stopped, any ball which has left the lawn is placed on the boundary where it went off.
11. If at any time a boundary ball obstructs the playing of another ball, the boundary ball may be temporarily removed. If the replacing of a ball on the boundary is prevented by the presence of another ball which will be played first, then the ball is replaced after the obstructing ball has been played. Otherwise the obstructing ball is temporarily removed until the ball is played.
12. A ball may be jumped over a hoop or another ball.
Hoop Point
13. A ball scores a hoop point by passing through its next hoop in the order and direction shown in the diagram. This is also known as running a hoop.
14. A ball begins to run a hoop when any part of it first emerges from the back of the hoop, and finishes doing so when the whole of it finally enters the front of the hoop.
15. A ball may take more than one turn to complete the running of a hoop.
16. If a ball other than the striker’s ball is knocked through the next hoop in order, then the hoop is scored for the side owning that ball. If more than one ball runs a hoop in the same stroke, the ball which was closest to the hoop at the start of the stroke is deemed to have scored the point.
17. If a ball runs two hoops in the same stroke, then both hoop points are scored.
Balls played out of sequence or by the Wrong Player
18. Players should stop play (known as 'forestalling') if they think a wrong ball is about to be played or has been played in the last stroke.
19. If the striker plays the wrong ball of their side in singles, or, in doubles, the striker's partner plays their own ball instead of the striker playing the correct ball, the opponent decides whether:
(a) the balls are replaced in their positions before the stroke in error and play continues by the right person playing the correct ball without penalty ("Replace and Replay") or
(b) the balls are left where they are, except that the ball just played is swapped with its partner ball. Any points scored are counted for the owner of that ball. The opponent then plays the ball that follows in sequence after the ball which should have been played in the last stroke ("Ball Swap").
20. Replace and Replay is the only remedy if a player plays an opponent ball or the striker's partner plays the striker's ball.
Playing for the next hoop
21. Players may play towards the hoop after the one being contested if desired, but should not go more than halfway otherwise the ball may become an 'offside ball'. Immediately after the hoop in order is run, any ball beyond the halfway line between the hoop just run and the next hoop in order is an offside ball, unless one of the exceptions in paragraph 22 applies.
22. Balls are not offside if they reached their position as a result of:
(a) the stroke just played, or
(b) a stroke played by an opponent, or
(c) contact with an opponent's ball, or
(d) being directed to a penalty area.
23. If a ball is an offside ball, the opponent(s) can decide to have it placed in one of the two penalty areas, from which it is played in its next turn. The penalty areas are semi-circles with a radius of 1 yard centred on the half-way points on the East and West boundaries.
Faults
24. The striker must hold the mallet by its shaft and swing it so as to attempt to hit the ball cleanly with an end face of its head. A fault is committed if, when playing a stroke, the striker:
(a) touches any ball with their body or clothing, or
(b) causes their mallet to touch any other ball, or
(c) hits their own ball more than once (known as a 'double tap'), or
(d) squeezes their ball against a hoop or the peg (known as a 'crush'), or
(e) plays a stroke in which their mallet causes actual damage to the court sufficient to deflect a ball played over the area.
25. If a fault is committed the striker's turn ends and the opponent decides whether the balls are left as they lie or replaced to their positions before the stroke was played. No points can be scored for the striker's side by a stroke in which a fault is committed but the non-striking side can score a point provided the balls are left where they lie.
26. If the striker attempts to play a stroke but misses the ball they intended to hit (known as an 'air shot') and does not commit a fault, the attempt can be made again.
Other Forms Of Play
Handicap Games
Advantage Play is an alternative handicapping system to Extra Strokes.
In Advantage Play, the starting scores are adjusted depending on the players' handicaps so that the stronger player may have to score more than 7 hoops to win a 13-point game and the weaker player fewer than 7 hoops. In a closely contested game, it may be necessary to play more than 13 hoops to get a result.
In doubles, the handicaps of the two players are added together and divided by two (halves are rounded up).
More information is available here.