Transcendental numbers are numbers that cannot be the zero of polynomials with rational coefficients. Most numbers are transcendental but proving that a specific one is transcendental is often a difficult problem. The auxiliary function method is a general recipe to show such results. This method uses a tool coming from geometry of numbers called Siegel's lemma. In this talk, we are going to explain how Siegel's is used in transcendence theory and prove the lemma using Minkowski theorem. If time permits we will discuss generalizations of Minkowski's theorem and Siegel's lemma to number fields and function fields.