Start with spaced dots, then fill the gaps. Watch the "bumpy" potential smooth out. This visualizes the limit as sum becomes integral.
Draw a long straight line. Notice the equipotentials form parallel cylinders. The potential decays slower than a point charge.
A cross-section of a uniformly charged spherical shell. The potential is constant inside, so the field (-∇V) is zero there.
Fill in a solid shape. This represents volume density ρ. Far away, the complex shape's potential looks just like a single point charge.