Rules of both variants are given here.
When a piece takes another piece, its gets the movement abilities of the piece it has taken. For instance, if a white rook takes a black knight, the white rook turns into a white knight. (The best is to use a second set and indeed change the piece to the actual piece.)
When a king takes a piece, it also turns into that kind of piece, but it stays royal. I.e., if a king takes a pawn, it can only move as a pawn, but it stays the piece that must be mated. If that king/pawn reaches the last row of the board, the king/pawn can be promoted to a king/queen, so now the opponent must mate a piece with the abilities of a queen - until, of course, that queen also takes a piece, etc.
Castling is only allowed with the original rooks, under normal castling rules.
Whenever a piece takes another piece, it gets the movement capabilities of that piece in addition to those it already had. So, if a rook takes a bishop, that piece can effectively move like a queen. A piece can accumulate the capabilities of several pieces. There are a few special rules:
Pritchard recommends playing this game in progressive fashion, e.g., by postal play.