As of March 13, 2020, interest on all federally held student loans will be waived for at least 60 days. Privately held loans are not eligible.
Monthly payments will stay the same and are expected to be paid if at all possible. The Department of Education will automatically adjust the interest, so it should show up on your next invoice.
You should contact your loan servicer to determine if your loans are eligible. (Loan servicers are to whom you make your monthly payment: Nelnet, Navient, etc.)
To suspend payments, you can ask for an administrative forbearance, which allows you to temporarily stop making payments without becoming delinquent. If you are in Public Service Loan Forgiveness or Income-Driven Repayment forgiveness, the time spent in administrative forbearance will not be counted toward the minimum payments you are required to make.