Check with a knight and attack the queen
Black to move
Solution
One solution line: Nf4+.
Position analysis
What happens on the board after the solution.
The key idea
Nf4+. The knight on f4 checks the king on e2 and attacks the queen on d3. It can take the queen after every reply (Ke3 → Nxd3; Kf2 → Nxd3+; Kf1 → Nxd3; Ke1 → Nxd3+; Kd1 → Nxd3; Kd2 → Nxd3). The material gain is verified over this short exchange.
The knight fork
A single knight move can create two threats.
A square that attacks both targets
Mark both targets and find a square from which a knight attacks both. Then check whether your knight can reach that square in one legal move.
When the fork gives check
A fork with check forces the opponent to deal with the check first. Look for a legal capture of the knight, then see whether you can take the queen after each reply.
Evaluate the position after the capture
After a capture, count the remaining material and look for threats. A fork can win an advantage, but the position after the exchange determines what that advantage is worth.
Sources
Check and king safety
How to identify check and test the legality of a reply.
King safety after a move
Check your own king after the move you are considering. A pawn can leave a file and expose its king to a rook check even if the king was safe before the move.
Pinned pieces
A pinned piece still attacks squares according to its movement rules. Count those attacks when testing a king move or castling.
Reading the line of check
Locate the checking piece first. If the check travels along a line, test whether it can be blocked. Then check captures and king moves.
Sources
Sources · CHESSDORRA