Controlled dielectric breakdown is becoming the main solid-state nanopore fabrication technique worldwide. This paper presents the construction of a system for the fabrication of a single solid-state nanopore in a membrane using this technique. We include a basic introduction to nanopore theory. We also detail the building process of the low-cost equipment for nanopore fabrication, so that this paper can be used as a guide for building a similar system. Finally, we include the results of the creation of two nanopores and their characterization.