A DNA metabolic process that results in the formation of G-quadruplex DNA structures, in which groups of four guanines adopt a flat, cyclic Hoogsteen hydrogen-bonding arrangement known as a guanine tetrad or G-quartet. The stacking of several layers of G-quartets forms G-quadruplexes, in which one or more DNA single strands are assembled in parallel and/or antiparallel, with interactions that can be either intra- or intermolecular in nature.