Once you have such a function f(x,z), the goal is to use a raytracing setup to render the image and do other effects as shadows or reflections. That means that for a given ray with some starting point in space (like the camera position) and a direction (like the view direction) we want to compute the intersection of the ray and the terrain f. The simplest approach is to slowly advance in the ray direction in small steps, and at each stepping point determine if we are above of below the terrain level.