The formation and evolution of dark spin-wave envelope solitons have been studied in a yttrium iron garnet (YIG) film. The Brillouin light scattering (BLS) technique has been used to map the propagation and evolution of the excited dark solitons. Experiments have been carried out using (1) a YIG-film delay-line structure supporting propagation of backward volume spin waves, (2) time- and space-resolved forward-scattering BLS, (3) a fixed magnetic field of 1000 Oe applied along the propagation direction, and (4) a soliton excitation technique based on the nonlinear interaction of two large amplitude cw input signals with fixed frequency enabling an induced modulation instability. Theoretical interpretation of the experiments based on numerical solution of the Ginzburg-Landau equation taking into account the conditions of nonlinear spin-wave dissipation is given. It is found that the dark soliton formation process involves competition between effects of nonlinearity and dispersion, and that nonlinear damping effects play an important role.