Basically, you have 2 options. One is to automate your response - if you look on the rhs of the card board you'll see a series of options - each is fairly well described. Click on one of these and the cards will be chosen to support that goal.
Crudely there are two dimensions - passive:aggressive; gain prestige:lose prestige
if we use this from my game as an eg:
The numbers that really matter are the first and third under each card. The first is the prestige stash (think of it as the pot for a gambling game) and the third is the crisis intensity. Closer this goes to 100 the chances of a war.
Across the top you can see the opening situation (you know this before choosing your cards), so this a relatively low prestige dispute (182) but quite high intensity (62)
In that I really did not want a war, so consistently picked cards that would defuse the crisis and - since I was prepared to lose to avoid a war - also wanted to keep the pot down. As it was I won the crisis by painting the beastly Prussians as aggressors to the rest of the world.
So in the end we got to:
Note that the first round pushed up the intensity as the Prussians played a very aggressive opening (it became 72), my more passive approach then calmed it down to 49 by the end - but at the cost of adding prestige (penalty for being a whimp).
So if you look over the card set, basically some will try to shift international support to you, some will add to the prestige pot and some will affect the crisis. If I don't mind a war, I'll be agressive but try to keep international opinion on my side, if I want a war - well insulting your opponent and mobilising will all increase tensions. If you really do not want a war, then being ultra-passive - indeed a bit of a whimp in the eyes of the other great powers is the way to go.
Get it wrong or right and you can see some massive prestige transfers. Or end up in a war you really never wanted.
What you can also do is to automate the basic card layout and then manually adjust according to your particular analysis.