The King is the tallest piece on a standard chessboard and usually has a cross-looking thing on top. It's usually represented by the letter "K". Just like Kings of old, this is the most important piece there is. The object of the game, in fact, is to capture the opponent's King.
It is also the weakest piece. The King can only move one square at a time, but he can move in any direction he likes.
The King on this board can move to any square right around him. (c6, d6, e6, e5, e4, d4, c4, and c5)
The Queen, (Q) on the other hand, is the strongest piece on the chessboard. She is the second tallest, and she moves in straight lines in any direction (horizontal, vertical, and along diagonals) as far as she likes, as long as nothing is in the way. A Queen placed on g2 on the above board could go to any square between and including a2 and h2, any square between and including g1 and g8, and also the squares h1, h3, f1, f3 and e4. If the King were not there, the Queen could move along the diagonal all the way to a8 if she liked.
The Rook (R) and Bishop (B) move in straight lines like the Queen, except the Bishop can only move diagonally and the Rook can only move horizontally and vertically. Now the Rook looks a lot like an old castle tower, and the Bishop is shaped like a pointy hat. Both can move as far as they like as long as nothing is in the way.
Now I said before that the last two pieces are weird. To review, the King moves one square in any direction, the Queen moves as far as she likes in any direction, the Rook moves horizontally and vertically as far as it likes, and the Bishop moves diagonally as far as it likes.
The Knight (N) is shaped like a horse's head, and it is the only piece that cannot be blocked by anything. The Knight moves in a little L shape... two squares horizontally or vertically and one the other. It always lands on a square that is the opposite color of the one it started on.
Spot's mark the spots that the Knight can go to. Note that they are all black squares and the Knight is already on a white square. If anything stood between the Knight and the spots, it wouldn't matter. The Knight could leap where it liked.
The Pawns (p) are like the frontline of chess. Technically these aren't pieces, but who's counting. You have eight of them to start the game with. These guys are the short ones that start on the second row for each side. They can only move forward, and only one square at a time. On any Pawn's first move, though, it can move two squares. If a Pawn gets all the way to the last rank, it becomes a Queen, Rook, Knight, or Bishop, at the choice of the player. Since the Queen is the most powerful, players almost always "queen" the Pawn. It is possible, though not likely, to have your original Queen plus eight more on the board at the same time through the queening of Pawns.
Unlike draughts, there is no such thing as "jumping" in chess. In order to take one of your opponents' men, you move your piece onto the square where your opponent's piece sits and remove his from the board. This is called "capturing". In the diagram below, the Queen, the Rook, and the Bishop could all take the Pawn on f7.
Using long algebraic notation, we would write down this move as b3xf7, meaning that the piece at the square b3 takes the one on f7. This is how computers keep this notation, and it is the way that leaves the least room for errors, but most players simply put Bxf7 (short algebraic notation), meaning the Bishop (capital B) takes the man on the f7 square.
If the Pawn were not there, and the Bishop moved to f7 instead of capturing something there, it would be written b3f7 or Bf7, meaning the piece at b3 moved to f7 in the first instance and Bishop moves to f7 in the second. In short algebraic notation, the Pawn symbol is often missed out all together, so that e4 means move a Pawn to e4 and dxe4 means the d Pawn takes the man on e4.
Every man on the board, except the Pawn captures by moving in the same way it always does. The Pawn, however, can only capture something that is one square to the left or right of his normal destination. Anything in front of it keeps it from moving. If two Pawns meet head on, neither makes any progress until a capture allows the path to open.
The Pawn can be compared to a small soldier carrying a shield in front of him that is so tall that he can't see where he's going or hurt the guy in front of him. Anytime an enemy appears around either side of that shield, though, he attacks.
This diagram shows a white Pawn at e4 and black Pawns at d5, e5 and f5. The white Pawn would normally move to e5 on its next move, but the black Pawn at e5 is blocking its path, so it cannot move there. It can, however, capture the Pawn at f5 or d5.
Now unless it is close to queening, the Pawn is the least important man. Most players agree that Bishops and Knights are worth about three Pawns, but Bishops are usually preferable to Knights since they can move farther. Rooks are worth about five Pawns and Queens are worth about nine.
That's how the pieces move. There are just a few more minor rules you should know about.