For those that play chess and want to improve their game, reading algebraic chess notation is essential.  It is not difficult to learn and will allow you to read and follow games in addition to keeping track of your own games.

Keep in mind the following guidelines are for Standard Algebraic chess notation.  There are a number of other systems which are used, though this system is the most widely used and the one you will likely see, perhaps except for a few players and games in older chess books.

• Each move refers to a place on the board. Familiarize yourself with the grid system, where a-h correspond to the files (vertical) from left to right and 1-8 correspond to the ranks (horizontal) from bottom to top (from White's point of view). a1 and h8 are the lower-left hand and the upper-right hand squares, respectively.
• Every piece, except for the pawn, is represented by a letter: king - K, queen - Q, rook - R, bishop - B, knight - N.
• The pawn does not have a letter. Therefore, if the move is "e4" it signifies a pawn move to e4.
• If two of the same pieces can move to a square, either the rank or file is used to determine which piece was moved. For instance Ngf3 or N5f3 would identify a particular knight, depending on whether the rank or file specifies the piece.
• Pawn promotion is signified with the "=" sign. a8=Q would signify a pawn queening on a8.
• Check and checkmate are signified by + and and #, respectively (sometimes checkmate is also "++")
• Captures are represented by "x".
• Kingside castling is 0-0 and queenside castling is 0-0-0.
• When a pawn captures en passante, e.p. is used.
• At the end of game, a white win, black win, and draw are respectively signified by 1-0, 0-1, and 1/2-1/2.

Practice writing and following chess notation.  A good way to start is by going over games online, where you can read the notation and the board will automatically update itself, so that you can test if you are familiar with notation.  Once you learn you will be much more confident and be able to use it in your games.