A mate in one is the first thing to look for in any position: a check the king cannot escape. Look at every check you have. For each, ask where the king could go, what could take the checking piece, and what could block the check. When the answer to all three is nothing, it is mate.
Below are three puzzles from the Lichess puzzle database, from easier to harder. Each one is solved move by move, with what every move does and what the line wins.
Puzzle 1: rated 971
Black has just played 14...Ng8, the arrow on the diagram. White to move and mate in 1. Lichess rates this puzzle 971, from 15,910 attempts. Try it before you read on, or set it up on a board.
The solution
- 15.Qg7#: the queen goes to g7, and it is checkmate.
It ends in mate in 1. The queen on g7 gives check to the king on h8. Black's own pieces stand on g8 and h7. The pawn on f6 covers g7.
Puzzle 2: rated 1,119
Black has just played 18...Kh7, the arrow on the diagram. White to move and mate in 1. Lichess rates this puzzle 1,119, from 16,216 attempts. Try it before you read on, or set it up on a board.
The solution
- 19.Qxg7#: the queen takes the pawn on g7, and it is checkmate.
It ends in mate in 1. The queen on g7 gives check to the king on h7. The queen on g7 covers g6, g8, h6 and h8. The knight on e6 covers g7.
Puzzle 3: rated 1,638
Black has just played 16...Nxb4, the arrow on the diagram. White to move and mate in 1. Lichess rates this puzzle 1,638, from 3,964 attempts. Try it before you read on, or set it up on a board.
The solution
- 17.Qxc8#: the queen takes the rook on c8, and it is checkmate.
It ends in mate in 1. The queen on c8 gives check to the king on e8. Black's own pawns and pieces stand on d7, e7 and f7. The queen on c8 covers d8. f8 is on the line of the check, behind the king, so the king cannot step there either.
Keep practising
The lesson Finding mate in one teaches the idea step by step, with positions to solve. GreyChess's rated puzzles come from the same Lichess database, sorted by theme and rating, so you can practise mates like these at your own level.