http://en.wikipedia.org/wiki/Article_Two_of_the_United_States_Constitution#Clause_1:_Command_of_military.3B_Opinions_of_cabinet_secretaries.3B_Pardonshttp://en.wikipedia.org/wiki/War_Powers_ResolutionHere's the real meat of it, also from wiki:
American presidents often have not sought formal declarations of war, instead maintaining that they have the constitutional authority, as commander in chief (Article Two, Section Two) to use the military for "police actions".
In 1973, Congress passed the War Powers Resolution, which requires the president to obtain either a declaration of war or a resolution authorizing the use of force from Congress within 60 days of initiating hostilities. Its constitutionality has never settled.
Since World War II, Congress has formally authorized all the major military engagements that the US has undertaken. (Vietnam, Lebanon, Panama, Persian Gulf War, Afghanistan, and Iraq.)
Some legal scholars maintain that all military action taken without a Congressional declaration of war (regardless of the War Powers Resolution) is unconstitutional; however, the Supreme Court has never ruled directly on the matter.
There is also much debate about the meaning of the word "declare". Some scholars suggest that to declare war does not necessarily mean to commence war. During the Philadelphia Convention, there was some discussion about the difference between the power to "make war" and the power to "declare war", and which of the two should be written into the Constitution. A declaration of war lets the citizens of a nation know that they are now at war with some other nation or entity. It also puts the belligerent nations and their citizens on notice. More importantly, this establishes that international law governs the conduct of the war. This protects citizens in all the warring nations involved insofar as if they are captured by the enemy, they will be treated as prisoners-of-war instead of mere criminals.
http://en.wikipedia.org/wiki/War_Powers_Clause