Endgames are where club players give away the most points relative to the effort it would take to fix. A dozen positions and a handful of rules cover most of what happens when the queens come off. You do not need a thick book. You need these ideas to be reliable under a ticking clock.
Activate the king
In the opening and middlegame the king hides. The moment the queens are exchanged, it becomes a fighting piece worth roughly a minor piece in the center of the board. The player who centralizes the king first often gets a decisive advantage in pawn endings and a serious one in rook endings.
The practical habit: after a queen trade, before you do anything else, ask where your king wants to be and start walking it there. Most players wait several moves too long.
The opposition
Two kings facing each other on the same file with one square between them are "in opposition." The player who does not have to move has the opposition, and in king and pawn endings this usually decides the game.
FEN
8/8/4k3/8/4K3/4P3/8/8 w - - 0 1With White to move, every king move is answered by the mirror: 1.Kd4 Kd6, 1.Kf4 Kf6. Pushing the pawn does not help either: 1.Kd4 Kd6 2.e4 Ke6 3.e5 Ke7! 4.Kd5 Kd7 5.e6+ Ke7 6.Ke5 Ke8 7.Kd6 Kd8 8.e7+ Ke8 9.Ke6 and it is stalemate. The key defensive move is 3...Ke7, stepping straight back so that when the pawn gives check the king can retreat in front of it.
With Black to move, Black has to step aside, and White's king walks past: 1...Kd6 2.Kf5 Ke7 3.Ke5 Kd7 4.Kf6 Ke8 5.Ke6 Kd8 6.Kf7 and the pawn runs home.
Rule of thumb: the attacking king wants to reach a square two ranks in front of its pawn. Those are the key squares. For a pawn on e3 they are d5, e5, and f5. Get your king to one of them and the pawn promotes regardless of who is to move.
The square of the pawn
When a passed pawn races against a lone king, you do not need to count moves. Draw an imaginary square with the pawn's path to promotion as one side. If the defending king can step inside that square on its move, it catches the pawn.
FEN
8/8/8/2P5/6k1/8/8/7K w - - 0 1With Black to move, 1...Kf5 enters the square and after 2.c6 Ke6 3.c7 Kd7 4.c8=Q+ Kxc8 it is a draw. With White to move, 1.c6 redraws the square from c6 to e8, the Black king on g4 cannot reach it, and the pawn queens.
Remember that a pawn on its starting square can move two steps, so count its square from one rank further forward.
The Lucena position: how to win rook and pawn versus rook
If you learn one rook ending, learn this one. White has the pawn on the seventh rank with the king in front of it, and the Black king is cut off on the far side.
FEN
1K6/1P1k4/8/8/8/8/r7/2R5 w - - 0 1The plan has three steps. First, check the Black king one more file away: 1.Rd1+ Ke7. Second, put the rook on the fourth rank: 2.Rd4. This looks slow, but it is the whole idea. Third, bring the king out: 2...Ra1 3.Kc7 Rc1+ 4.Kb6 Rb1+ 5.Kc6 Rc1+ 6.Kb5 Rb1+ 7.Rb4, and the rook blocks the checks. The pawn promotes next move.
The technique is called "building a bridge," and the rook on the fourth rank is the bridge. If you try to run with the king without it, the checks never end.
The Philidor position: how to draw rook and pawn versus rook
The mirror image. You are a pawn down, your king is in front of the pawn, and the enemy king has not yet reached the sixth rank.
FEN
4k3/1R6/r7/4K3/4P3/8/8/8 b - - 0 1The defending rook sits on the sixth rank and refuses to leave. White's king cannot step onto d6 or f6, so the only way to make progress is to push the pawn, and that is exactly what Black wants: 1...Rc6 2.Kd5 Rh6 3.e5 Rg6 4.e6 Rg1! 5.Kd6 Rd1+ 6.Ke5 Re1+ 7.Kf6 Rf1+ 8.Ke5 Re1+. Once the pawn is on e6, the White king has no shelter from checks along the files, because the pawn is in front of it and the Black king on e8 guards the squares beyond. If the White king walks away toward the rook, the pawn is left behind and falls.
Two things go wrong in practice. Players drop the rook to the first rank too early, before the pawn reaches the sixth, and the king walks to d6 or f6 with a winning position. Or they leave the rook on the sixth too long and get mated after the pawn arrives. The trigger is the pawn: when it reaches e6, the rook goes back.
Rooks belong behind passed pawns
Tarrasch's rule: whether the pawn is yours or the opponent's, put your rook behind it. Behind your own passed pawn, the rook gains squares every time the pawn advances. Behind the enemy pawn, the rook ties the opponent's rook to the pawn's defense. A rook in front of its own passed pawn is the worst case, because it has to move away for the pawn to promote.
Bishop versus knight, briefly
With pawns on both sides of the board, the bishop is usually better: it covers both wings from one square. With pawns on one side only, or with pawns fixed on the bishop's color, the knight is at least equal and often stronger. Before entering a minor-piece ending, look at where the pawns are and which color they sit on.
The wrong-colored bishop
A bishop and a rook pawn (a- or h-pawn) cannot win against a lone king if the bishop does not control the promotion square and the defending king gets to the corner.
FEN
7k/8/5K1P/8/2B5/8/8/8 b - - 0 1This is worth knowing as both a drawing resource when you are down material and as a trap to avoid when you are converting. If your extra pawn is a rook pawn and your bishop is the wrong color, keep another pawn on the board or steer the enemy king away from the corner before trading.
Do not rush
Endgames reward patience more than any other phase. If you have a winning position and no immediate way to force matters, improve your worst-placed piece, restrict the opponent's king, or fix a pawn weakness. The side with the advantage can usually afford a few waiting moves; the side without it often cannot.
Make it stick
Learning these positions once is not enough. Set them up against the engine and play them out. The position analysis tool lets you paste any of the FENs above and check your plan against Stockfish. Then look at your own games: run them through Game Review and look specifically at the endgame accuracy. If it is noticeably lower than your middlegame figure, you know where the easy points are.
The checkmate puzzles will sharpen the last step, and for a full review method see how to analyze your chess games.