Gentzen proved a famous cut elimination theorem using constructive methods. It is also possible to prove it non-constructively, with a conceptually simpler argument, but a constructive proof is important for a number of reasons. I will present the constructive argument for cut elimination, for classical propositional logic, formulated using tableaus. This is purely expository; there is nothing new. But it is a proof that every logician, or logician-to-be, should know, and I will cover the basics using a detailed set of slides which will be made available afterward, on my web site.