I am working with a student in their home and being paid by check from the parents. This is via a government agency. How do I declare it, I have no forms.

You are an independent contractor so would complete Sch C. 

It depends whether you report it as self-employed or an employee of the people you work for. If you qualify as an employee, they must issue you a W-2.

People who work around your house under your direction are generally household employees. These include housekeepers, maids, babysitters, gardeners, and others. Contractors (like repairmen or plumbers) and other business people who work for you as independent contractors, aren't your household employees. The main difference is that you control what household employees do and how they do it.

If you pay a household employee cash wages of $2,300 or more for 2021, then you need to withhold and report both Social Security and Medicare taxes from their pay. You generally must withhold 6.2% of Social Security and 1.45% of Medicare taxes (for a total of 7.65%) from all cash wages you pay to that employee. You also must pay your share of Social Security and Medicare taxes, which is also 7.65% of cash wages. (Cash wages include wages you pay by check, money order, etc.) Unless you prefer to pay your employee's share of Social Security and Medicare taxes from your own funds, you should withhold 7.65% from each payment of cash wages you make to the employee and pay this amount, along with your matching share, to the IRS.