We know that a conductor must have all of its net charge sitting on a surface. In this case, its the outer surface of the sphere. Furthermore, we know the electric field is the same as for a point charge sitting at the center of the sphere for points which are outside the sphere. Inside the sphere, the electric field is zero since any Gaussian surface we draw which is completely contained inside the sphere would contain no net charge. If we set the origin of our coordinate system as being at the sphere center, then we need to integrate the electric field over a path (it might as well be straight-line since that's the easiest to integrate) from infinity to the sphere and from the sphere surface to 0 (since the electric field is different inside than outside).