It is rare that blowing something up solves a problem - but when it comes to objects with singularities, it turns out to be a good approach! In this talk, I will outline the method of blowing up a singularity of an algebraic variety in order to produce a new variety. This new geometrical object will have very similar properties, but with the added benefit of being less singular, or even smooth. Along the way, I will introduce the notion of projective space and how embedded objects can be seen using charts. Unlike my own research, this geometry can be visualised easily and so there will be plenty of pictures and nice examples to see how blowups work.