This paper sets forth a thorough procedure to design surface-mounted permanent magnet synchronous generators. Since synchronous generators generate the majority of electrical energy, their relevance in society nowadays is substantial. As a consequence, the methodology to design these electrical machines also holds great importance. However, even though a considerable amount of works addresses the matter, it is difficult to find a complete and thoroughly explained design procedure. The proposed method is based on analytical equations to fully consider PM generator fundamentals with a few simplifications, which implies in a considerable number of design equations and parameters. Differently from most papers on the design of PM synchronous generators, a significant level of detail and explanation is presented, all design choices are discussed, and the suggested ranges for the design parameters are shown. This results in a straightforward procedure that allows non-experienced designers to easily replicate the results and effectively enhance the comprehension of permanent magnet synchronous machines, and provides a guideline for researchers from other fields who may need to understand and perform a synchronous generator design. To show the effectiveness of the proposed design procedure, a PM generator is designed, and the results are compared with a finite element simulation, showing good accuracy.