How to Read Chess Notation
Chess notation is a way to write a move so that anyone can replay it. The form used almost everywhere now is algebraic notation. Files are the letters a through h, left to right from White's side. Ranks are the numbers 1 through 8, nearest to furthest from White. The bottom-left corner of the board, from White's perspective, is a1. Black's king starts on e8.
Squares and piece letters
A pawn move is written as the square the pawn lands on: e4 means the pawn that could go to e4 went there. Other pieces use a capital letter. N is knight, B is bishop, R is rook, Q is queen, K is king. Nf3 means a knight moved to f3. English notation uses N for knight because K is already the king.
When two pieces of the same type could reach the square, the notation adds the file or the rank that tells them apart. Nbd2 is the knight from the b-file moving to d2. R1e1 is the rook from rank 1 moving to e1.
The symbols
x means a capture. Bxf7 is a bishop capturing on f7. + means check. # means checkmate. O-O is kingside castling and O-O-O is queenside castling. Those are the letter O, not the number zero. A promotion is the arrival square plus the new piece: e8=Q. En passant is written as a normal pawn capture, sometimes with the letters e.p. after it.
A move number belongs to the pair. 1.e4 e5 means White's first move is e4 and Black's reply is e5. 1...e5 with the dots means you are starting in the middle of the line, and e5 was Black's first move.
A line to replay
Set up a board and play this Italian Game fragment one move at a time.
1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.c3 Nf6 5.d4 exd4 6.cxd4 Bb4+
Move by move: both sides put a pawn in the center, both sides develop a knight toward the center, both sides put a bishop on the dangerous diagonal, White prepares d4 with c3, Black develops the other knight, White strikes in the center, Black takes on d4, White recaptures with the c-pawn, and Black's bishop moves to b4 with check. If your board matches that description after six moves each, you can read notation.
The ideas behind those moves are in the Italian Game and in the rules of chess.
Marks you will see in books
! is a strong move. ? is a mistake. !? is an interesting try, and ?! is a dubious one. You do not write these on your own scoresheet during a game. You write the moves. The punctuation is commentary added later.
Keep a scoresheet when you play slowly. The habit is what lets you look at the game afterward and see the moment the position changed, instead of remembering only the last tactic.
Frequently Asked Questions
Why does my app use little pictures instead of letters?
Figurine notation replaces N, B, R, Q, and K with piece icons. The squares and the symbols x, +, and # stay the same. If you can read letters, you can read figurines.
Do I have to write the pawn's file when it captures?
Yes. Pawn captures include the file they came from: exd4, not xd4. That is how you know which pawn did the taking.
What about old descriptive notation?
Older books say things like "P-K4" for e4. You can ignore it until you need a specific old book. Algebraic is the notation used in every modern article, database, and scoresheet.
Replay one line until it is easy
Then replay a game you played. The squares will stop being a code. When you want to see what a written move is worth, put the position on the board and ask chess hints.
Try the line on the board with chess hints.