Spin foam theory is a concrete framework for quantum gravity where numerical
calculations of transition amplitudes are possible. Recently, the field became
very active, but the entry barrier is steep, mainly because of its unusual
language and notions scattered around the literature. This paper is a
pedagogical guide to spin foam transition amplitude calculations. We show how
to write an EPRL-FK transition amplitude, from the definition of the 2-complex
to its numerical implementation using \texttt{sl2cfoam-next}. We guide the
reader using an explicit example balancing mathematical rigor with a practical
approach. We discuss the advantages and disadvantages of this approach and
provide a novel look at a recently proposed approximation scheme.
