Suppose White has a king, queen, and pawn, and Black has a king and pawn. Also, suppose the kings are connected since otherwise White will mate easily with the queen. White's pawn is not needed to win (see "King and Queen vs. King and Pawn") but its presence requires certain technique. The difference between this ending and that of "King and Queen vs. King and Pawn" is that often the White pawn does the job of blocking the Black pawn and the White pawn often limits the manouverability around the Black pawn. Otherwise the technique is pretty much the same. It is very common in this ending for the two pawns to oppose each other (like White pawn on e4 and Black pawn on e5). I call these locked pawns. It turns out that no matter where the locked pawns are, White can always win this ending. First, consider:
8/8/8/8/3p4/3P4/7Q/6kK w
White to Move and Win
Here, Black is forced to keep the kings connected. White's
goal is to attack the Black pawn with his queen, then to lead
the Black king toward that pawn with his own king, and
finally to rush his own king away from the pawn, leaving
the Black king behind to get caught in an explosion.
The White queen can attack the Black pawn from anywhere,
and it's useful to explore how White can win in various
ways. We will now look at one simple way in which White
can win: 1. Qf4 . This is a useful
square from which to attack the pawn. Now White will slip
his king up through the "hole" (e4) between the Black pawn
and White queen. The Black king will be forced to follow
if he wants the kings to remain connected, and an explosion
will wait for him. 1. ... Kg2 2. Kg1 Kf2
3. Kg2 Kf3 4. Kf2 Ke2. Note that Black cannot
play 4. ... Ke3 because of 5. Qxd4##. Black might like to
get to e4 (the hole) first with his king to try to prevent
White from leading him through, but he cannot--he cannot
get next to his Black pawn first without subjecting himself
to explosion. Play continues: 5. Ke3 Kf3
6. Ke4 Ke3 7. Ke5+ (or Kd5+) Ke4 8. Kd6+ Kd5 (or Ke5)
9. Qxd4##. We'll call this winning method "leading
Black through the hole." It's also instructive to see that
White cannot win by leading Black
8/8/4k3/4K3/3p1Q2/3P4/8/8 w
White to Move
Here, White might try: 1. Ke4 Ke5 2. Kf3+
(Ke3 is not available) Ke4, and now
whether White moves his king to e2, f2, or g2, Black can
follow safely with Kf3. So, the Black pawn is preventing
White from winning as he did when he went
I would now like to show you that "leading Black through the hole" is not the only way to win this type of ending. In fact, if the locked pawns are near the center of the board, the White queen can be placed so as to attack the Black pawn from anywhere. Consider the next diagram:
3Q4/8/8/8/3p1k2/3P1K2/8/8 w
White to Move and Win
Here, I have placed the queen on d8, but as you play through the moves, notice how it doesn't really matter where the White queen is (as long as she is attacking the Black pawn and the kings aren't bumping into her). White's plan is to lead the Black king over the top of the pawn and rush down one of the sides. Once the White king gets to d5, the Black king will try to be on d6 (having the opposition) in order to be as flexible as possible (but in the end it won't matter). So, Black will try to stay "on top" of the White king, that is, Black will retain the opposition that he now holds. But first, let's see what happens when the Black king follows passively behind: 1. Ke4 Kf5 2. Kd5 Ke5 3. Kc4 Kd5 4. Kb3+ Kc4 5. Qxd4##. That was easy. Let's now see a little more resistance: 1. Ke4 Ke5 2. Kd5 Kd6. Now, rushing down doesn't work: 3. Kc4+ Kc5 4. Kb3 Kb4 and, thanks to the opposition, the Black king is safe. So, instead, White plays a clever waiting move to gain the opposition: 3. Qd7!. Actually, any queen move, like 3. Qh4, that keeps an eye on the Black pawn would work. Now Black must commit to one side of the pawns or the other, and whichever way Black goes, White will run down the opposite way. For example: 3. ... Kc5 (or 3. ... Kc6) 4. Ke4 Kd5 5. Kf3+ Ke4 6. Qxd4##.
Keep in mind that in the previous ending, White had plenty of room to manouver. If the locked pawns are on a rook-file or knight-file, then White's options are more limited. Consider:
8/8/p1Q5/P1K5/2k5/8/8/8 w
White to Move and Win
Here, White should lead Black up through the hole to win: 1. Kb6+ Kc5 2. Kb7+ Kb6 3. Ka8+ Kb7 4. Qxa6##. This technique will work as long as the Black pawn is on its third rank or farther advanced, no matter what file the pawns are on. But if the Black pawn is on its original square, then White needs other methods to win. Consider:
3Q4/p1K5/P1k5/8/8/8/8/8 w
White to Move and Win
Here, White will strip the Black king away by moving his king to a8 and queen to b8. This is very similar to the technique in "King and Two Queens vs. King," but this time the Black pawn on a7 (instead of a White queen) helps to strip away the Black king. Play proceeds: 1. Kb8 Kb7 2. Ka8 Kb8 (2. ... Kc6 3. Qc7+ Kb7 4. Qb8 Kc6 5. Qb7+) 3. Qc8 Kb7 4. Qb8 Kc6 5. Qb7+ and White will mate with the queen.
If the pawns are near the center, White has a choice of techniques. Consider:
8/3p4/2KP4/2k5/4Q3/8/8/8 w
White to Move and Win
Here, White can march his king to d8 and then put his queen on c8 to evacuate Black off the c7 square, or he can "lead Black through the hole" by placing a queen on b7, or he can just attack the Black pawn from anywhere. For example: 1. Qa4 Kb6 2. Kc7 Kc6 3. Kd8+ Kc7 (3. ... Kd5 4. Qe4+) 4. Ke8+ Kd8 5. Kf7 Ke8 6. Qxd7##.
Ok, now we've seen how to win this ending no matter where the locked pawns are located. What happens if the pawns are not locked? Well, if the pawns are sufficiently far apart then White can win as in "King and Queen vs. King and Pawn" (he can simply ignore his own pawn). But sometimes the pawns are close together and the White pawn can get in the way. But still the technique is easy and similar to the ideas presented above. For example, consider:
8/8/8/3p4/8/2k1P3/2K1Q3/8 w
White to Move and Win
Here White can proceed with: 1. Qb5 Kd3 2. Kc3 Kc2 3. Kd4 Kd3 4. Kc5+ Kc4 5. Kd6+ Kc5 6. Ke7+ Kd6 7. Qxd5##. White has other winning methods as well.