Techniques and strategies for discovering and measuring the properties of Higgs bosons via s-channel production at a µ + µ − collider, and the associated requirements for the machine and detector, are discussed in detail. The unique feature of s-channel production is that, with good energy resolution, the mass, total width and partial widths of a Higgs boson can be directly measured with remarkable accuracy in most cases. For the expected machine parameters and luminosity the Standard Model (SM) Higgs boson h SM , with mass < ∼ 2m W , the light h 0 of the minimal supersymmetric Standard Model (MSSM), and the heavier MSSM Higgs bosons (the CP-odd A 0 and the CP-even H 0 ) can all be studied in the s-channel, with the heavier states accessible up to the maximal √ s over a large fraction of the MSSM parameter space. In addition, it may be possible to discover the A 0 and H 0 by running the collider at full energy and observing excess events in the bremsstrahlung tail at lower energy. The integrated luminosity, beam resolution and machine/detector features required to distinguish between the h SM and h 0 are delineated.