The most important thing to do is to take the complaint seriously, no matter how angry it makes you or how farfetched the allegations seem. Investigate the complaint thoroughly and, if you find any merit to the complaint, remedy the situation as quickly as possible. For practical strategies to avoid workplace discrimination complaints, get The Essential Guide to Handling Workplace Harassment & Discrimination, by Deborah C. England (Nolo). For more information about handling complaints of discrimination, see Nolo's article Guidelines for Handling Discrimination and Harassment Complaints.
Do not discipline or demote the employee who complains. Most antidiscrimination laws contain a provision that prohibits employers from retaliating against employees who complain of discrimination or participate in an internal investigation of a complaint. Both firing and discipline constitute retaliation, as do lesser actions. To learn more about what constitutes retaliation and how to avoid it, see Nolo's article Preventing Retaliation Claims by Employees.