Horses move like a Knight in Chess, except that they can't jump over other pieces. They step outward on a row or column, then diagonally outward one step. If something is adjacent to a Horse on a row or column, it can't move in that direction. Elephants move diagonally two steps. However, Elephants cannot jump over other pieces, so an Elephant is blocked in any direction where another piece is diagonally next to it.
Chariots move like the Rook in Western Chess, that is, any number of squares along a row or column.
Thus to capture they leap over the intervening piece and land on the enemy piece, like a cannonball. One account of Xiangqi dates the introduction of the cannon at AD 839. The Mandarin must stay confined to the fortress, and can only move a single step along the diagonal lines shown. This gives it only 5 possible positions. This piece is often translated into other names such as Assistant, Guard, Counsellor, and Officer.