If you use the 'building blocks' idea queen endgames are the
foundation. To understand and play the majority of endgames with any
confidence knowledge of them is required. By the time a queen endgame
is reached the result of the game is usually no longer in any doubt
(assuming the right knowledge from the players) and the battle is
probably over, won or lost.
When I'm playing out a queen endgame I feel that it's more a
procession than a game. Little or no thinking is generally required,
just memory and pattern recognition, assuming you know the information
given in this section...
King and Queen vs. King:

FEN: 8/8/4k3/Q7/4K3/8/8/8
|
The result of this position depends on who's to move. With black to move he can draw by moving the kings together,
connecting them.
1...Ke5!

FEN: 8/8/8/Q3k3/4K3/8/8/8
|
-
1...Kf5! and
1...Kd5! also draw.
Now white has no way of separating the kings and so is
unable to win e.g.
2.Kf3+ Ke4 3.Kg2 Kf3 4.Kh1 Kg2 5.Qg5 Kg1 6.Qg2 Kh2 etc
However if it's white to move he can play
1.Ke3!

FEN: 8/8/4k3/Q7/8/4K3/8/8
|
- or
1.Kd3! or
1.Kf3! which prevents black from connecting the kings, forcing an easy win e.g.
1.Ke3 Kf6 1.Qe5+ Kf7 2.Qf6+ Ke8 3.Qe7# 1-0
King and 2 Queens vs. King:

FEN: 8/8/8/4k3/4K3/8/8/QQ6
|
Here white is winning whoever is to move, a long as he knows the correct technique. This technique can be split into 3 stages.
Stage 1: Place your king on a corner square...
1.Kf3+ Ke4 2.Kg2+ Kf3 3.Kh1 Kg2

FEN: 8/8/8/8/8/8/6k1/QQ5K
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Stage 2: Place your queen on the squares of the corner's short diagonal, in this case
g1 and
h2, while ensuring that it's black's move afterwards...
4.Qg1 Kh2 5.Qh8! Kg2 6.Qh2 Kf3

FEN: 8/8/8/8/8/5k2/7Q/6QK
|
Stage 3: Checkmate!
7.Qgg2+ Ke3 8.Qf4+ Kd3 9.Qc2#

FEN: 8/8/8/8/5Q2/3k4/3Q4/7K
|
This technique is used in other situations too:

FEN: 7Q/8/8/8/8/8/p7/Kk6
|
1.Qh1 Kc2(
1...Kb2 2.Qb1 is a faster win for white)
2.Qc1+ Kb1 3.Qc2 Kb2 4.Qb1

FEN: 8/8/8/8/8/8/pk6/KQ6
|
Kc3 5.Qb2+ etc. 1-0
Creating a Path for the King:

FEN: 8/8/8/4p3/4K3/4k3/8/7Q
|
The technique used by white here is the most common winning method
in queen and pawn endgames and therefore all endgames. The most
important idea is the positioning of the queen.
General idea is to put the queen to attack the black pawn in such
fashion that you will be able to allow the queen to take the pawn at
the right time exploding opponent's king while yours can pass it by.
1.Qh6 Kd3 2.Qe6

FEN: 8/8/4Q3/4p3/4K3/3k4/8/8
|
White creates 2 'paths' around the black pawn that his king can now take.
After
2...Ke3 either:
3.Kd5 Kd4 4.Kd6
Kd5 5.Ke7+ Kd6 6.Qxe5#
or
3.Kf5 Kf4 4.Kf6 Kf5 5.Ke7+ Kf6 6.Qxe5# win for white.
This technique might be a bit tricky at first, but as you play more
and more such endings, it will go easier and easier, and same goes to
other endings. Practice and more practice.
The Opposition:
I believe the idea of the opposition was found
quite recently by Rekursiv (a strong atomic player from FICS). The idea
is very rare in practise but worth knowing.

FEN: 8/8/8/8/4k3/4K3/4p3/4Q3
|
With black to move he loses, but with white to move he draws due to
the opposition. Black does this by moving onto the square directly in
front of white’s king each time it moves(or queening if white’s queen
moves).
e.g.
1.Kf2 Kf3 2.Kg3 Kg4 3.Kf4 Kf5 4.Ke5 Ke6 5.Kd6 Kd7 6.Kc7 Kc8 7.Kb8 Kb7!

FEN: 1K6/1k6/8/8/8/8/4p3/4Q3
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Black still has the opposition. Black can moves in front of the
king again if it moves away from the 8th rank, but otherwise it can
stay on the 7th.
Note that black could have done this earlier to no cost e.g.
4...Ke4, however he must be careful as sometimes it loses e.g
2...Kg2??

FEN: 8/8/8/8/8/6K1/4p1k1/4Q3
|
3.Kf4 Kf3 (
3...Kg3 4.Kg4! with the opposition)
4.Qxd2 1-0.
Generally it’s better to keep things as simple as possible and stay in front of the stronger sides' king.
But with black to move white reacts to which way the king moves, drawing it around the pawn e.g.
1...Kd4 2.Kf2 Ke3 3.Kg1

FEN: 8/8/8/8/8/4k3/4p3/4Q1K1
|
or
1...Kf4 2.Kd2 Ke3 3.Kc1

FEN: 8/8/8/8/8/4k3/4p3/2K1Q3
|
both being 1-0...
Part 3:Pawn endgames