We describe the fabrication and assembly of the first prototype 201. 25 MHz copper cavity for the muon ionization cooling experiment (MICE). This cavity was developed by the US MUCOOL collaboration and will be tested in the new MUCOOL Test Area at Fermilab. We outline the component and subassembly fabrication steps and the various metal forming and joining methods used to produce the final cavity shape. These include spinning, brazing, TIG welding, electron beam welding, electron beam annealing and deep drawing. Some of the methods developed for this cavity are novel and offer significant cost savings over conventional methods.