The typical strategy is to advance the pawns on the opposite flank to open up lines for your rooks to attack your opponents castled position. Bearing this in mind, it's helpful to try and entice your opponents pawns to advance. If you can achieve this before you castle on the opposite side, you can win yourself a tempo or two to increase your chances in such a position. There are occasions when it is ok for you to lose a tempo, perhaps by pinning your opponents knight to tempt them into advancing a flank pawn. Once you castle on the opposite side the advanced pawn becomes a target... 😉
As said before, there is a advantage to attack first. One essential thing to consider then is that sacrifices are more likely to be made in these situations. You can of course consider bishops and Knights sacrifices on pawns, for tactical purposes. You can also consider to sacrifice a rook for a good minor piece (see the game against pawn riot, with a rook and pawn against a minor piece, and still the game is considered about even).
But above all, think about pawn sacrifice. It is generally good to sacrifice a pawn to open the enemy king file. Even if you don't have clear tactical project, exchanging a pawn against an open file on the king (or nearby) can really be worth it. it will considerably open your possibilities; sometimes such sacrifice will be declined (cause somewhat paradoxically, your pawn defends his king from rooks and queen...) enabling you to speed up your attack.
Defensive strategies are more likely to loose. then, the general strategy when you're attacked is: not to flee, not to suppress the threat, but to create a bigger threat on the other side.
That said, you still have to play defensive or positionnal moves. Generally speaking, try to close the pawn structures on your side; try to make defense moves which also place active pieces for a subsequent attack (such as fiancetto bishops). Taking the center is not as necessary as in other games. it should be a secondary objective. Try to get it while doing other things...
It is great to have long files and diagonals that enable you to attack and defend at the same time.
see my game here for instance
Game 5702163
Finally, think that in these sharp games, the actual position becomes relatively more important than the theoretical value of pieces (pawn 1, Knight 3, etc)
I am not a very good player, so my advice may be arguable. This is the way I try to do things though...