You need to deduct only income taxes from student's paychecks. Do NOT deduct Social Security, Medicare or federal unemployment taxes.
Please assist your student(s) in applying for a Social Security number. They do NOT actually need the number before they can begin to work. As long as they have applied, or intend to apply, they can work for you. Most payroll services will allow a “dummy” number to be entered into their system until the student gets his or her number. It may take a long time for the Social Security number to be issued, due to delays in the Social Security system.