If the Black king is in the centre, then the fastest way to win is to box Black's king in until it is on one of the edges of the board, then use your queen to cut the black king off and force him to stay on the back rank/file, then bring your king up and deliver checkmate.
With a White king on a1, a black king on e5 and a white queen on c1, the following is an example of how to box Black's king in:
1.Qc4 Kf5 2.Qd4 Ke6 3.Qc5 Kf6 4.Qd5 Kg6 5.Qe5 Kf7 6.Qd6 Kg7 7.Qe6 Kh7 8.Qg4 followed by Ka1-b2-c3-d4-e5-f6 and mate.
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