Two of you share one army. Your side's turn passes back and forth: Player one moves, the opponent replies, Player two moves, the opponent replies, and around again. One position, one result, two people steering it.
Nothing changes. Every piece moves the way it always has, on the board it always has. Castling, en passant, promotion, check and mate — all standard. White moves first.
No conferring. Player one and Player two do not discuss the position, point at squares, or sigh meaningfully. The game will not stop you; nothing here enforces it. The whole question is what happens to a plan when it has to survive somebody else's turn.
One person against two, or the computer at one of three settings. Either way they take every second move, so they see the position twice as often as either of you does.
Player one moves. The opponent replies. Player two moves. The opponent replies. Around again.
Player one and Player two share one army, one position and one result, and never move twice in a row. Every piece behaves exactly as it does in ordinary chess.
House rule: no conferring. Nothing here enforces it.