I guess, broadly, there are two types of attacks, one where you need a pawn break to open some lines, and one where you can just shove 3, 4, or 5 pieces in front of the enemy king, sacrifice to open lines, and checkmate via pure force.
So the first thing I'd hate to see in an opposite side castling game is that 1 or more of the pawns in front of my king have moved. That makes it much easier for pawn storms to open lines, and somewhat easier for piece sacrifices to open my king too.
Umm, there are all sorts of things that can go wrong... including you could be winning for 39 moves and then blunder on move 40. It's hard to give advice if you don't share a game.
It seems to me that whenever my opponent castles on the opposite side than me (which in the vast majority of cases means that my opponent castles queenside while I castle kingside), I end up losing the game, no matter how I try approaching the situation. If I try to hurry to attack my opponent's king, it always feels like I just lose the race because somehow my king gets attacked first. If I try to add defenses to my king, it rarely helps anything. Just trying to play "normally", without rushing to attack or defend doesn't seem to help much either (because my king gets attacked relentlessly).
What are the principles on how to play when castling on opposite sides?