In this talk I will introduce the ideas of singularities of a polynomial and resolution of those singularities, and then develop the blowup process algorithm. For a polynomial f, a point is singular if f and all its first partials vanish at that point. A resolution of the singularities of f gives a non-singular polynomial g related to f via birational maps. The blowup process provides an algorithm to produce g and these maps. Over R^2, examples are easy to visualize which in turn makes understanding the core ideas easy, so the talk will be accessible to all.