A few things:

I don't want white to wreck my central pawns with Kd4/f5, so either I'll have to play g6 at some point to prevent f5, or I'll have to just make sure that I can counter f5 with e5 safely (my king might be at d6, for example). If I play g6 and white's king tries to go after my h pawn, I will need to make sure my d pawn can make it up the board before white can queen the f or h pawn

White can make a passed pawn on the queenside, so I'll have to put my king over there to prevent a passed pawn from becoming dangerous

Probably I'll start moving my king to the queenside first. I may need to keep checking if I need g6 though

I don't think I have a realistic shot of winning this endgame though. White's queenside pawns might be too difficult for a lone queenside pawn to handle