After Pearl Harbor, the United States declared war on Japan as an act of self-defense. Hitler, not even aware that Japan was planning such a strike, declared war on the United States on December 11, 1941. The United States had long criticized German aggression in Europe but few people wanted to fight another world war on the continent, especially after the squabbling that took place after WWI. Roosevelt realized that Germany would be a threat to U.S. security in the future, so he negotiated Lend-Lease agreements with Britain. British Prime Minister Winston Churchill soon stated that German submarines were sinking American goods going to Britain. When American destroyers started escorting British supplies, Germany and America fought an unofficial naval war on the Atlantic before December 7, 1941.
To answer your question concisely, America fought Germany because it viewed Germany as a threat to its Allies, its markets, and perhaps one day itself. German submarines had already shown a capacity to attack in American coastal waters, and Roosevelt (correctly) viewed a war against Germany as a war for the nation's survival.