Taxis are expensive, but rental cars are available at the airport. And they'll pick you up, too, for the return run.
Railways are reliable and go to both northern and southern shores of Lake Balaton.
They vary in price. Hungary's Tourinform provides a booking service and can advise on what is available. The home page of Siofok has information in English and German. Hungary's Lake Balaton is a popular respite E-mail this story to a friend.