Searches for sterile neutrinos in nuclear processes rely on the identification of subtle deviations from Standard Model expectations in precisely measured energy spectra. In this contribution, we present the analysis methodology adopted by the CUPID-0 experiment to investigate sterile neutrino emission in double beta decay. We discuss the characterization of the expected spectral shapes, the construction of a model including the signal hypothesis, and the Bayesian statistical framework used to extract constraints on the active-sterile mixing angle $\sin^2\theta$. Particular emphasis is given to the treatment of spectral correlations and systematic effects, which play a key role in spectral-shape studies.