We review the method of producing adiabatic optical micro- and nanofibers using a hydrogen/oxygen flame brushing technique. The flame is scanned along the fiber, which is being simultaneously stretched by two translation stages. The tapered fiber fabrication is reproducible and yields highly adiabatic tapers with either exponential or linear profiles. Details regarding the setup of the flame brushing rig and the various parameters used are presented. Information available from the literature is compiled and further details that are necessary to have a functioning pulling rig are included. This should enable the reader to fabricate various taper profiles, while achieving adiabatic transmission of ∼99% for fundamental mode propagation. Using this rig, transmissions ranging from 85% to 95% for higher order modes in an optical nanofiber have been obtained.