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Due to the current state of things, you are no longer required to make any payments whatsoever on your federal student loans until September 30th of 2020. Interest cannot accrue during that time either and not paying will not effect your credit score in any way.
This only applies to federal student loans that are currently held by the federal government though, which accounts for ~88% of all loans. If you have a private student loan, like a Sallie Mae or even some FFEL Program and Perkins loans, you will still be required to make payments on those loans. Be sure and check with your lender to see if you qualify for this or not.
The CARES Act that was just signed into law orders all lenders and collection agencies in charge of federal student loan payments to halt any attempt to collect student loan payments for the next 6 months. And when they start up again they have to give you 6 notices when payments are required to start up again. So this isn't something you have to sign up for. It is something agencies and companies are required by law to do.
You are still allowed to make payments on your loans during this time though, and the good news is anything you do pay for the next 6 months goes purely to your principle balance.
Also if you were getting your income garnished or your tax refund was being reduced due to student loan collections, that is also being suspended for 6 months.
All these effects take place immediately. And it's possible Congress will take further action in regards to student loans in the future. Democrats were at first trying to push for various forms of Student Loan Forgiveness but that did not make it into this current stimulus package. However they are expected to meet up again starting April 20th so it is possible for more relief in the future. Or an extension of suspensions.