Convert surface normal to screen-space (you always want the sphere map to be mapped in screen-space).
Use this normal as UV coordinate to sample from texture. The ss. normal will probably be in -1 to 1 range, while UV's are in 0-1 range. Plus, the normals need to start sampling from the center of the texture.
So, divide surface normals by 2 to scale them into a range of 1, then add 0.5 to them to translate them to the center.
Then just use only the X and Y components as UV's coordinates to sample.
Should be all there is to it save for some details.