Declaring war on another civilization will give you a penalty in dealing with other civilizations in the game, called the warmonger penalty. This reflects other leaders’ mistrust or fear of your actions. The most common way to declare war, and the method by which all warmonger penalties are computed, is the Formal War. In this, a civilization first denounces a target civilization and then declares a Formal War.
The warmonger penalty increases with each era, as war becomes a less acceptable solution to the disagreements between the civilizations of the world. The warmonger penalty is also modified by the kind of war you declare. In most cases, declaring war and capturing an enemy city will give you that era’s warmonger penalty, and razing a city will give you three times that era’s warmonger penalty. Certain Casus Belli (see the section on Casus Belli under Diplomacy) may modify these warmonger penalties, reducing them for certain actions, or making them more expensive. Other actions, like using nuclear weapons, will modify your warmonger penalty as well.
The other approach is to denounce the opposing civilization first and then declare war formally. With this avenue to war, the warmonger penalties are NOT increased and there is the opportunity to use a Casus Belli to reduce those penalties. However, because you must first denounce your opponent, such a plan is "telegraphed" for the target and you will not have the advantage of surprise.