When Congress passed the CARES Act on March 27, 2020 to provide an economic relief package to the country, it didn't just include "bailouts" to the Airlines and other industries, and the much-talked-about PPP loans to small businesses. It also created a Pandemic Unemployment Assistance ("PUA") program to extend unemployment benefits to those who traditionally will not qualify for unemployment benefits.
One is traditional unemployment, available as it always has been to those who lose their jobs through no fault of their own. The CARES Act additionally provides an additional $600/week for up to 39 weeks that you will automatically (eventually) receive, if you are on unemployment due to COVID.
The second the PUA. This program is funded by the federal government, not any employer you work(ed) for, and is available to independent contractors, self-employed individuals, others not traditionally covered, as well as specific COVID-related situations.
It will depend when your state implements these new programs as to 1) when you will begin to receive the $600 extra per week or 2) when you can apply for the PUA. Wisconsin is in the process of implementing this program and has kept its website up-to-date with information.
If you are eligible for traditional unemployment, you should apply now. If you are eligible for PUA, check your state's unemployment website for details how and when to apply.
You should receive back pay for any eligible weeks under the CARES Act to receive the $600 extra or the PUA funds.
The below information is from the State of Wisconsin. However, the second page is information about the Federal Programs and will apply to all states.