The model specifies a mapping from an ideal picture on a rectangular grid where the scene is projected in a rectilinear way to a distorted picture on another rectangular grid. It tells you where the pixels that should have appeared at some coordinate (x,y) can be found in the distorted image that you actually have. The problem is then that the gray values you need a some location in the corrected image can be found according to the mapping at some factional value, so you need to use interpolation.
Also, you need to take into account that one pixel in the corrected image will, in general, cover an area in the uncorrected image that is different from the area of one pixel in the uncorrected image. The gray value of the pixel in the corrected image is then determined by demanding that the total amount of light that falls in the area is the same as the light that fell in the corresponding area in the uncorrected image.