This site makes every effort to explain everything in words, but when describing a series of chess moves it often is convenient to use abbreviations to describe them. Those abbreviations are known in chess as notation. This site generally uses the “algebraic” notation employed in most chess books, though with a small difference explained below. Despite the unpleasant label, it's very easy to understand. Most of it can be figured out as you read, but here is what you need to know about how it works:
1. Squares are named by their coordinates—a4, e5, h8, etc.; these should be self explanatory, since every diagram includes numbers running up the side of the board and letters along the bottom. The numbered horizontal rows are called ranks. The vertical columns named by letters are called files.
2. Pieces are named by their first letter. Q = queen; R = rook; etc. The only exception is the knight, which is referred to as “N” to distinguish it from the King (“K”). Pawns are named by their squares, so that “d4-d5” means the pawn on d4 moves to d5. Sometimes in this book (and routinely in other books) a pawn move is described without bothering to name the square it came from: one simply says "1. d5," and everyone understands this means that the pawn on the d-file moves to d5.
3. Captures are described with an “x” between the names of the pieces capturing and being captured. So QxB means queen takes bishop; Rxa5 means the rook captures the pawn on a5; and h7xN means the pawn on h7 captures the opposing knight.
This last point is the way that the notation here varies from the usual algebraic notation in other books. Algebraic notation normally describes a capture by just referring to the square where it occurs. Thus if White’s queen takes Black’s rook on the f6 square, most chess books would say “Qxf6”; but on this site we will say “QxR.” The reason for the difference is that this site is meant primarily for people who haven’t read other chess books before (as noted before, it's a chess book for people who don't like chess books), and for that audience the notation used here will be more intuitive. It's easy to understand that “QxB” means “queen takes bishop”: easy to imagine, and easy to find on the board. “Qxf6,” however, has to be translated into “queen takes bishop” by looking at the board, finding f6, and seeing what piece is there. That’s easy when you know instinctively where f6 is, but most readers of this project probably will find it faster to locate the bishop than to locate f6. The real benefits of naming captures by the squares where they occur come when describing long sequences, and few of the sequences here will be all that long. (The approach used here is similar to the one used in Bobby Fischer Teaches Chess, a well-executed book for beginners.)
This approach to describing captures should be easy to follow for readers already used to ordinary algebraic notation; anyone can understand what QxB means even if they are used to reading Qxf6. The gripe I anticipate from those who get worked up about these things is that if readers become used to this approach they will find it hard to read algebraic notation in other books: they will see, say, “Qxf6” elsewhere and have trouble remembering that the other author means to say the queen captures whatever piece is on f6, not that the queen captures the f6 pawn (as it will mean here). I regard this as a trivial complaint; the reader of this site who does move on to other books should have no trouble making the transition if the above explanation is kept in mind (or just figuring it out on the fly; for this explanation makes the whole business sound more confusing than it is in practice). It's not that big a deal.
4. Turning back to the notation rules, castling is indicated by writing 0-0 (if it's on the side of the board where the king starts) or 0-0-0 (if it's on the queenside: long castling, as it is called).
5. Now a couple of minor points that don't come up often; you probably don't need to worry about them, but for the sake of completeness: if a capture is made en passant, that's indicated by writing "ep" afterwards or some variant. (I'm assuming you know what an en passant capture is, but if you don't, I'll explain it if it ever gets used here—and in the meantime you easily can find an explanation of it elsewhere on the web.) Second, if one of your pawns reaches the opponent's back rank, it gets promoted to some other more powerful piece of your choice—usually the queen, though very occasionally some other choice works better. We indicate promotion with an equal sign: f7-f8=Q means the pawn on f7 moves to f8 and becomes a queen. Again, I'll say more about this wherever it pops up.
Finally, if more than one piece could be indicated by a description (in other words, if I refer to "R" but there are two rooks on the board and it's not obvious which one is meant), sometimes the coordinate of the piece will be given as well. So Rc8xN means the rook on c8 (not some other rook) captures the opponent's knight. Occasionally this approach also will be used just for clarity's sake even if there is no technical reason for confusion.
6. Sequences of moves are described in pairs, with the White move first. Thus a game might begin 1. e2-e4, e7-e5 [again, this could have been written "1. e4, e5"]; 2. Nf3, Nc6; 3. Bb5, a7-a6; 4. BxN, d7xB. This means that White started by moving his e-pawn forward two squares, and that Black then did the same; then on White’s second turn he moved his knight to f3, and then Black moved his knight to c6. White brought out his bishop. Black chased it with his pawn on the a-file. White replied by taking Black's knight. Black recaptured with pawn on c6. The position on the left illustrates the result.
When we look at positions from the middle of a game (as we generally will) we will describe White’s first move in that position with the numeral “1” (as something like “1. Nf5,” for example). We call it “1” because it’s the first move in the pictured position, even though it’s not the first move in the game.
If we want to start by describing a move of Black’s, we do it by saying something like: “Black can play 1. …Nf5.” The “1” followed by the three dots indicates that we’re looking at the first pair of moves in the position but that we’re starting with the second half of the pair: in other words, with Black’s move.
7. A plus sign after a move (like this: Rh8+) means that the move checks the enemy king. A "#" sign after a move (like this: Rh8#) means that the move is checkmate (or simply “mate,” as we more commonly say).
8. It often happens that a player can sacrifice a knight or bishop to win an enemy rook. Since rooks are more valuable than knights or bishops, a player who does this is said to have “won the exchange.” If we reach a stage of the game where I have, say, a bishop and a rook and you have a bishop and a knight, I am said to be “ahead the exchange.”
9. A piece is said to be “loose” if it has no defenders. It is “hanging” if it is exposed to capture; you hang your queen if you leave it where your opponent can take it for free. This also is known as leaving a piece en prise.