(i) For two equal and opposite point charges (a dipole): field lines start on the positive charge and curve around to end on the negative charge (denser near the charges). Equipotential surfaces are a family of surfaces everywhere perpendicular to these field lines — closed, egg-shaped surfaces enclosing each charge individually near the charges, and the perpendicular-bisector plane between the charges is the $V=0$ equipotential surface.

(ii) If $E$ had any component along the equipotential surface, then moving a charge along that surface would require work $W=qE\cos\theta \cdot d \neq 0$. But by definition, all points on an equipotential surface are at the same potential, so no work is done in moving a charge along it ($W=q\Delta V=0$). This is possible only if $E$ has no component along the surface — i.e. $E$ must be perpendicular (normal) to the equipotential surface at every point.