There are two Quest types. In the first group you’ll find quests that appear on the Campaign Map and you decide when you want to deal with them. The other quests require your immediate attention: they pop up as messages and you have to deal with the given situation in that round.
In Battle quests you have to fight a battle against someone. Diplomacy quests outline certain political situations where you have to make decisions: the sub-screens contain the various paths you can take to solve the problem. Right below your possible choices you can see the resulting consequences: if you only see a question mark, it means that the outcome is dubious.
Adventure quests are very simple: you get a description of the situation at hand and several options about the given circumstances.