Why algebraic notation replaced older systems
Chess was once commonly recorded in descriptive notation, which described moves relative to each player's own side of the board and required different labels depending on which color was moving. Algebraic notation uses one fixed grid for the whole board, which is shorter, unambiguous, and is now the standard used in essentially all modern chess publishing and software.
Reading a full game score
A full game is written as a numbered sequence of move pairs, White's move followed by Black's response, like "1. e4 e5 2. Nf3 Nc6." Once the individual symbols are familiar, following an entire recorded game or replaying a famous match becomes a matter of working through the list one pair at a time.
Frequently Asked Questions
Why is the knight written as "N" instead of "K"?
"K" is already used for the king, so knight uses "N" instead to avoid confusion between the two pieces.
What does it mean when two pieces could make the same move?
Notation adds a disambiguating letter or number from the starting square, such as Nbd7 (specifying the knight starting from the b-file), when two knights could otherwise both move to d7.
Do I need special software to read algebraic notation?
No — once you know the symbols, you can read it directly from a book, a website, or a scoresheet, though many people also use a physical or digital board to follow along visually while reading a game.