Unemployment insurance is a joint system of federal and state law. Federal law sets the general parameters of the program; the federal government also collects some of the money for the program and makes additional benefits available during times of high unemployment.
However, most of the details are determined by state law, including:
As you can see, you'll need to find out your state's rules in order to figure out your eligibility and apply for unemployment. Fortunately, most states make lots of information available to unemployment claimants online, through their state's unemployment insurance agency. Click on your state, below, for a link to its unemployment agency.
District of Columbia