Pieces names refer to the way they capture, which is described later.
There is also a new piece : the immobilizer, represented by an upside-down rook.
Pawns move as orthodox rooks, and the king moves as usual, one square in any direction. All other pieces move like an orthodox queen.
When a piece is adjacent to an enemy immobilizer, it cannot move unless the enemy immobilizer is adjacent to a friendly immobilizer or chameleon (cancelling the powers of the opponent's immobilizer).
Note : this corresponds to the "pure rules" described on this page , which slightly differ from the initial rules. The aim is to get rid of the weird suicide rule by weakening the immobilizers lock. In particular, in the original rules two adjacent immobilizer are stuck forever until one is captured. Note that it's still the case if all chameleons disappeared.
Easy case first: the king captures as usual, by moving onto an adjacent square occupied by an enemy piece. But this is the only piece following orthodox rules, and also the only one which captures by moving onto an occupied square. All other pieces capture passively: they land on a free square and captured units are determined by some characteristics of the movement.
Note: the immobilizer does not capture.
If at the end of its movement a pawn is horizontally or vertically adjacent to an enemy piece, which itself is next to a friendly piece (in the same direction), the "pinced" unit is removed from the board.
Imagine that rook and king of the same color are two corners of a rectangle (this works if these two pieces are unaligned). If at the end of a rook move an enemy piece stands in any of the two remaining corners, it is captured.
A knight captures exactly as a queen in international draughts game: by jumping over its enemies, as many times as it can/want but always in the same direction. In this respect it is less powerful than a draughts' queen: on the following diagram c8 or f6 cannot be captured. However, the knight does not have to maximize the number of captured units (as is the case in draughts).
The queen captures by moving away from an adjacent enemy piece, in the opposite direction (without jumping, the path must be free).
The chameleon captures pieces in the way they would capture. So, it
...and these captures can be combined.
Remark: the move indicated on the diagram doesn't capture the black pincer on e5, since it is a diagonal move (not like a pawn).
Besides, chameleon immobilizes immobilizers (but cannot capture them since they do not capture).
A chameleon captures the king in the same way the king captures, which means that a chameleon adjacent to a king gives check.
The game ends by checkmate or stalemate as in standard chess. Note however that checks are more difficult to see, because of the exotic capturing rules. For example, on the following diagram the white king cannot move to e5 because then the black pawn could capture by moving next to it.
The Wikipedia page is a good starting point.