The depth buffer method is used to determine visibility in 3D graphics by testing the depth (z-coordinate) of each surface to determine the closest visible surface. It involves using two buffers - a depth buffer to store the depth values and a frame buffer to store color values. For each pixel, the depth value is calculated and compared to the existing value in the depth buffer, and if closer the color and depth values are updated in the respective buffers. This method is implemented efficiently in hardware and processes surfaces one at a time in any order.