How do I convert the game into KQK easily, or simply mate? I've already learned the Philidor position.
Unfortunately, no "easy" fool-proof method is known. It can take 31 moves until the checkmate or capture the rook with best blay from both side in the worst possible initial position. Nevertheless, the queen can always win if the player with the rook has no perpetual check or a fast win of the queen or a stalemate trap.
In particular, you have to avoid stalemate traps. Human defence tends to lose faster because of the fear of putting the rook far away.
A difficult position is, for example W : Kd5, Qf7 S : Kd8, Rb6
where white has to find the counterintuitive move Qf4! which is not the only winning move but soon or later white must come to this idea to win.