The results of modelling of the excitation and propagation processes of exchange spin waves (ESW) in epitaxial films of yttrium iron garnet (YIG) are presented. It is shown that the origin of the efficient ESW excitation is magnetic inhomogeneity, which is always present in a thin transition layer at the interface between a magnetic film and a nonmagnetic substrate. It is found that the parameters of magnetic inhomogeneity significantly affect wave characteristics of the emitted ESWs. A method was proposed for employing ESWs to measure the magnetization distribution parameters over the thickness of the YIG film and the ESW dissipation parameter. The measured parameters were used to calculate the dispersion and attenuation of the ESWs, define their amplitude characteristics in continuous and pulsed regimes, and estimate their phase losses. It is shown that dissipative losses of ESWs are not significant. More significant losses can occur due to phase dispersion on non-parallel reflective surfaces of the YIG film. It is demonstrated that such phase losses can be significantly reduced by precision optical polishing of the YIG film samples.