The methods implemented in PyRate are described here:
Silvestro, D., Schnitzler, J., Liow, L.H., Antonelli, A. & Salamin, N. (2014) Bayesian Estimation of Speciation and Extinction from Incomplete Fossil Occurrence Data. Systematic Biology, 63, 349–367.
Silvestro, D., Salamin, N., Schnitzler, J. (2014) PyRate: A new program to estimate speciation and extinction rates from incomplete fossil record. Methods in Ecology and Evolution, 5, 1126–1131
A detailed manual can be found here. Please report suggestions and bugs to this email address.