If you are talking about an employee who gets a W-2, not a contractor, there is no simple "cheat sheet" that will cover all cases. As a general rule, it doesn't matter where the employee lives or where the business is located. What matters is where the employee works. For the specific states that you mentioned, if he works in Virginia you have to withhold Virginia income tax and any other applicable Virginia taxes, such as SUI or SDI. This will hold true in most cases, but a few states have special rules for telecommuters, and a few states have reciprocal agreements with neighboring states for employees who live in one state and work in the other.
A payroll service, or a local accountant or tax professional who does payroll work, should be able to help you with specific cases.
