Depends on the type of income.
If the income is received for wages reported on a W-2, they do not need to file since they are below the minimum filing requirements.
If the income is from self-employment they are required to file a tax return since the amount of SE income is $400 or more. They report the SE income and expenses on a Schedule C which is part of the federal tax return, Form 1040. If they do have to file then make sure they indicate on their tax return that they can be claimed as a dependent.
