Most of us do not have a need for a paternity testing service but if need be, there are certified DNA testing facilities out there. Some even offer Home DNA Testing in which the tested parties collect their own DNA samples and mail them to the laboratory. This is available in the U.S.
When you call to place an order, they will send you a DNA kit and explain the step-by-step completion process. Before ordering a home test, consider the Legal Test if you believe the results will ever be used beyond personal knowledge. This way, you won't have to purchase another test in the future.