How do you remove surface rust from an old rifle?

if it is a valuable shotgun you are trying to restore, use toothpaste. The abrasive material in toothpaste will be enough to remove surface rust without damaging the blue finish. If the rust is deeper, try an auto polishing compound... if it is real deep, use a 4" angle grinder. If you polish off the bluing, be sure to touch it up with cold blue or it will rust again.