The most fundamental duty of Congress is to make laws. These laws must be coherent in the role of the United States and must promote the execution of the Constitution of the United States. This may sound like Congress has unchallenged power but the included words like "necessary for the execution" and "provide for the common defense" makes it impossible for Congress to develop laws that violate any other part of the Constitution. Besides making laws, Congress also passes bills and debates current laws. All laws that Congress enacts must go to the President for review and approval.
Another basic law that answers the question "what are the duties of Congress" is that Congress shall have the ability to declare war. Now, they don't have control over declaring war and it's not a spontaneous decision because both houses and the President must approve the war.
Congress also has the duty to coin money. In more terms about money, Congress also has the duty to collect taxes and pay debts. Also, Congress must also provide enough money to provide a reasonable defense for the United States, which reads in Article I as "raise and maintain the military."
A duty that Congress often performs is the ability to override any Presidential vetoes. The majority must be in agreement, which involves a two-thirds vote from Congress.