The basic game mechanics of chess remain unchanged. Pawns move as pawns move, Kings move as kings move, and the little horsey guys do what little horsey guys do.
Here is where it gets interesting.
instead of being a two person game, Group chess requires at least three players on each side. If you can manage five players a side, do that. You can work out variations with fewer players if you must.
The Three Players
The Royalty: The person playing the Royalty can move only the King and Queen pieces. As the monarchy they get to send orders downward through their General.
The General: The person playing the General can only move the pawns. They receive orders from the Royalty as to the disposition of troops. Here is where it gets interesting. They can chose to ignore those orders and pass along orders of their own to the Rooks, Bishops, and Knights.
The Elite: The person playing the Elite can move only the Bishops, Rooks, and Knights. They receive orders from the General which have (maybe) been passed down from the Royalty. Just like the General can ignore the orders of the Royalty, the Elite may ignore the orders of the General. If you have enough players, get one person to pay the Rooks, one to play the Bishops, and one to play the Knights.
Let the chaos ensue.