I think what you are refering to is called "algebraic notation", which is
the method used on RHP to record moves.
With this system, each square on the board has a unique
letter/number identification. (similar to map grid co-ordinates) This is
always laid out exactly the same, and is easiest to visualize from
white's end of the board.
From white's perspective, the 'a' square is the first one on the left,
and going from left to right are a,b,c,d,e,f,g and h.
Going back to the 'a' square on the left, you can now give each of the
eight squares in the 'a' column or file a number. Starting in white's
bottom left corner, you have 'a1'. From there you count up to eight,
so you have black's king's rook starting on 'a8'.
To use this system to describe a move, all you do is record the
letter/number of the 'from' and 'to' square.
So, e2-e4 means that something was moved from the e2 square to
the e4 square. (At the start of a game, this would be white moving the
king's pawn forward two squares)
If black moves the black kings pawn forward two squares, that would
be shown as e7-e5.
If the above are the opening moves in a game, it may show up as:
1. e2-e4, e7-e5. (showing white's first move and black's reply)
Later in the game the same 'e2-e4' could be used again to describe a
move by either white or black.
Most basic chess books will describe this and other methods of move
notation much more clearly, I'm sure!
I hope this was helpful.