You hire an accountant to process the payments.
THEY will pay the employees, withhold the statutory withholding rates, deduct that pay from your business revenue to reduce your net profit, and calculate your business taxes accordingly.
The fact that you have to ask this question means you have absolutely no business processing your own payroll. you need to hire a professional NOW before you get yourself in trouble, bankrupt your company with IRS fines, and put yourself and all your employees out of work.
Think of it like insurance. You probably have an insurance plan that protects your business against things like fire, theft, etc. You're willing to pay those premiums to reduce your risk. Hiring a payroll processing company or an accountant is like insurance for your finances, it protects you against the risk of HUGE fines from the IRS if you screw up. In fact most payroll processing companies offer a guarantee that if they screw up and get you fined they will pay the fine.