Step 1: Picture it.
Imagine joining together all the points in a field region that happen to have exactly the same electric potential. The surface formed by these points is an equipotential surface, for instance concentric spheres around a single point charge or parallel planes for a uniform field.
Step 2: Deduce the work property.
Moving a test charge between two points on such a surface involves a potential difference of zero, so \(W = q\,\Delta V = 0\). No work is spent moving a charge along the surface.
Step 3: Deduce the field direction.
If the field had a component along the surface it would do work as the charge moved, contradicting \(W = 0\). Therefore the electric field must be entirely normal (perpendicular) to the equipotential surface everywhere.
\[\boxed{\text{Constant-potential surface; field is normal to it, } W=0}\]