This information from the Baker administration advises that people collecting regular unemployment benefits should start receiving the added $600/week this week. 
The Department of Unemployment Assistance is not yet able to process the benefits extended under the CARES Act to people in the gig economy, self-employed, and others not previously covered, but hope to begin compensating them beginning April 30.  We don't yet have a date for those who previously exhausted their benefits.

Federal Pandemic Unemployment Compensation (FPUC): An additional $600 per week for individuals collecting benefits from regular unemployment compensation will be added to unemployment benefits retroactive to March 29, 2020 and will begin being disbursed to claimants this week. 
Those receiving Pandemic Emergency Unemployment Compensation, Pandemic Unemployment Assistance, Extended Benefits, Trade Readjustment Act, and Disaster Unemployment Assistance will receive the additional $600 payments retroactive to March 29, 2020 as soon as their claims are processed and determined eligible.

Eligible claimants who are already receiving UI do not need to do anything for the additional $600 to be added to their weekly benefit amount. This benefit will be available for all new claimants filing for regular Unemployment Compensation as well, which can be done at www.mass.gov/unemployment/covid-19

Pandemic Unemployment Assistance (PUA): For Individuals Not Covered Under Traditional Unemployment Insurance (Self-Employed, Gig Economy Workers, Others):  This benefit will be available for individuals not covered under traditional unemployment insurance like the self-employed or gig workers or those who do not qualify for lack of wages. DUA is now working with a vendor to build a new platform to disburse those benefits. This platform is expected to begin processing claims on or about April 30, 2020.
Eligible claimants under PUA will be retroactively compensated with this benefit beginning February 2, 2020, or the first week a claimant was unable to work as a result of COVID-19, whichever date is later. 

Eligible claimants should continue to check for updates at www.mass.gov/unemployment/covid-19 on the new platform.

Pandemic Emergency Unemployment Compensation (PEUC): For Individuals Who Exhausted Previous UI Benefits:  This 13-week extension of benefits for individuals who exhausted their previous benefits is not yet available as DUA continues to await federal implementation guidance. Once implemented, the first week a claimant can be compensated on this benefit is the week beginning March 29.

DUA is committed to moving as quickly as possible to get workers the benefits they deserve during these unprecedented times and will continue to communicate with the public about the status of these benefit programs.  

Let me know how you are doing, and contact us at patricia.jehlen@masenate.gov if you have further problems. 

If you're trying to apply for Paycheck Protection, let us know about your experience.  We're trying to figure that out too.

Stay safe, and stay in touch,