Welcome to Quantum Chess! The rules are simple, I promise.
First off, all the pieces move like regular chess. Rooks move down a rank or file, bishops on the diagonals, horsies move in Ls, you get the idea.
However, there is an additional rule. When moving a piece, you can choose to either move it to a position it can travel to, or you may elect to capture an arbitrary amount of available captures (or castles). This can be performed by clicking targets instead of dragging a piece to them.
That is, instead of performing Rc4 or Rh4, you can perform Rc4&h4. However, doing so will put your piece into quantum uncertainty. All independent parts can operate on their own, but once a piece is "observed", its wave function will collapse.
This means if a piece is captured, its alternate positions will be proven to have just been captured, if a king is checked, unchecked kings will be proven to not exist, and if a pawn promotes, the matching pawns on the board will be proven to not exist.
Pieces can split multiple times, in one turn or over several. Checkmate occurs when a player is unable to remove one of their kings from danger on their turn.