What method requires the least amount of memorisation (doesn't have to be shortest path to victory) for the queen vs knight ending?
I have looked at tablebases but the moves are somewhat bizarre and it would be nice to have some simple logic to follow (even if it takes a few more moves to checkmate).
This is assuming the opponent is expert and will not make simple mistakes.
I have looked at tablebases but the moves are somewhat bizarre
That's the problem with tablebases; they're efficient but they can't 'play' human chess. This particular endgame is one-sided enough that it's almost never required to play the best move.
Just drive the opponent's king to the edge of the board, as you would do with king+queen vs. king; just be careful that you don't end up in a knight fork. If the knight gets too far away from its king, you can probably fork it yourself after a few checks. Once on the edge of the board, the reduced mobility of the knight and mating threats will eventually lead to defeat.
Here is an example (from Shredder Chess):
The 'human' move here is Qg6+ (or Qa6+) followed by Kd5; it doesn't matter that Qe2, Qe3 and Qe4 are one move faster.
Always keep your K and Q on opposite colour squares, or have your K diagonally 1 gap away from the N, so that you will never be forked.
Beyond that, just as Glorfindel said, fork the N if it's allowed or drive opponent's K to the edge and checkmate.
