Coordinates from a1 to h8 and algebraic notation
Every one of the 64 squares has an address. Files run from a to h, left to right as White sees the board, and ranks run from 1 to 8, starting on White's side. The square h1 is always light and sits in White's bottom right corner, which is a quick way to catch a board set up the wrong way round. A move is written as the piece letter followed by the destination square: K for king, Q for queen, R for rook, B for bishop, N for knight. Pawn moves carry no letter at all, so a pawn going to e4 is simply e4.
A handful of symbols complete the system. An x marks a capture, as in Nxe5. A plus sign means check, a hash means checkmate, O-O is kingside castling, O-O-O is queenside castling, and =Q shows a pawn promoting to a queen. Lichess, Chess.com, printed books, the articles in this hub and official tournament scoresheets all use the same notation.
Notation can feel dry at first, yet it opens up two abilities at once. Learners can follow an opening line like 1.e4 e5 2.Nf3 Nc6 3.Bc4 without needing a diagram, and they can record their own games to review later. A simple drill: point at random squares and call out their names for a few minutes, then write down the first ten moves of a recent online game from memory, without peeking at the move list.
Once squares and moves come out fluently, books, puzzles and your own games all become readable without anyone translating them for you.