If you've just hired a household employee, you are probably what the law calls a "household employer". 

If you hire someone to do domestic work such as child care, and you are able to control what work they do and how they do it, you are a household employer.  If the individuals who work for you are self-employed, however, you are not liable for any of the taxes discussed in this program.  Self-employed persons are in business for themselves.  An example of a self-employed person is the owner of a day care center where you leave your child.  This person would not be an employee of parents who use that center.  Also, people who work for you in your trade or business are not household employees.  An in-home household employee in virtually all cases will be considered your household employee.  Other types of household employees may include the neighbor who baby-sits for you on weekends, the person who cleans your house every week, or even the neighbor who cuts your lawn using your lawn mower and tools.

For more information on who is or is not an "employee" under the law, read Caregivers Who Are Not Your Household Employees and get IRS Publications 926, 937 and 15 (also known as Circular E).