How would one proceed to graph this type of complex equation? Is there a general way of proceeding?
Given two complex numbers $z$ and $w$, $|z-w|$ is the distance in the complex plane from $z$ to $w$.
With that in mind, a complex number $z$ satisfies your equation iff it is as far from the complex number $2i$ as it is from the complex number $2$. The set of all such points in the plane is a relatively easy thing to draw.