Helpnwith strategy to win thus end game

What strategy should I use to win this end game? I'm white and computer evaluates position as +6.

My own thought is that I need to capture the b7 pawn, without losing my own pawn (And not allowing him to get a promotion pawn of course). If I manage this I think the rest is not so difficult. And this(capturing the b7 pawn) is also what the computer finally does if I follow the recommended moves on both sides. 

Problem for me though is that I cannot understand the logic behind all of the moves that gets me to this position, to me it looks just like a bunch of random moves and the finally I am in a position where the queen can capture the pawn. But I could never have found these moves myself.

s there a understandable strategy I (as a 1000 rated player) can use here to convert this position to a win? Either by capturing the b3 pawn, or maybe with another strategy. I find it not too difficult to trade my pawn against all of his but then I have a pure ueen vs took endgame. Is this winning for white? And if so, how difficult is it? As I said I'm only 1000 level beginner.

EDIT: is it not possible to edit the topic of a post (I made a typo)?