It is widely understood that the curved shape of a typical airfoil (such as a Clark Y) causes a pressure difference that creates lift. How do symmetrical airfoils do this when the top and lower surfaces are the same shape and length?
By using a non-zero angle of attack. When the trailing edge is pointed downwards, and assuming the airstream leaves the trailing edge smoothly, the exiting airstream is deflected downwards. This causes lift via conservation of momentum. Increasing the angle of attack will increase your lift until such time as the airstream over the trailing edge becomes non-smooth. (When this happens, you're close to stalling.)
(Image from this page, which unfortunately appears to be down)
As you can see from the above graph, a symmetric airfoil at zero angle of attack generates no lift; see this site from NASA as well as the above Wikipedia page.