King and Two Queens vs. King

Suppose White has only two queens and a king and Black has only a king. This is always a win for the stronger side. First, if the kings are separated and can be kept that way, then the mate is easy and only one queen is required (though two are faster). See "King and Queen vs. King".

So, suppose the kings are connected. White can force the kings apart by achieving a setup. That is, he ignores Black and proceeds to set up his own pieces on specific squares. The setup White heads toward is king on a1 and queens on a2 and b1 (or the equivalent setup in any other corner of the board). Once his pieces are on those squares, the only safe square for the Black king is b2, from which he will be forced to move. For example, consider:

8/8/8/8/8/2QK4/3Qk3/8 w
White to Move and Win

1. Kc2+ Kd1 2. Kb1+ Kc1 3. Ka1+ Kb2 4. Qdc1 Kb1 5. Qa5 Kb2 6. Qb1 Ka2 7. Qa3 Kb2 8. Qaa2 (setup achieved) Kc3 9. Qbb2+ Kd3 10. Qc4+ Ke3 11. Qbe2#.

It is worth knowing how to mate in three moves like this after the setup is achieved in case you are low on time.

One thing worth cautioning you about is the possibility of accidentally stalemating your opponent in this ending. For example, consider:

Q7/8/8/8/8/8/kQ6/K7 b
Black to Move

If Black plays 1. ... Kb1 then White must avoid 2. Qaa2?? which results in stalemate. Instead he should proceed something like this: 2. Qaa3 Ka2 3. Qb1 Kb2 4. Qaa2 and the setup is achieved.