Refer to the IRS web site for Hiring Employees for complete requirements. In most circumstances, you'll need a Form I-9, Employment Eligibility Verification and a Form W-4, Employee's Withholding Allowance Certificate completed.
The I-9 is to certify that the employee is legally eligible to work in the United States.
The W-4 is used to let you know how much income tax to withhold from the employees' wages. You'll need this information when you add the new employee in the payroll application.