Self-assembling peptide-based hydrogels are a class of tunable soft materials that have been shown to be highly useful for a number of biomedical applications. The dynamic formation of the supramolecular fibrils that compose these materials has heretofore remained poorly characterized. A better understanding of this process would provide important insights into the behavior of these systems and could aid in the rational design of new peptide hydrogels. Here, we report the determination of the microscopic steps that underpin the self-assembly of a hydrogel-forming peptide, SgI37-49. Using theoretical models of linear polymerization to analyze the kinetic self-assembly data, we show that SgI37-49 fibril formation is driven by fibril-catalyzed secondary nucleation and that all the microscopic processes involved in SgI37-49 self-assembly display an enzyme-like saturation behavior. Moreover, this analysis allows us to quantify the rates of the underlying processes at different peptide concentrations and to calculate the time evolution of these reaction rates over the time course of self-assembly. We demonstrate here a new mechanistic approach for the study of self-assembling hydrogel-forming peptides, which is complementary to commonly used materials science characterization techniques.