Rogerson, Shimer & Wright (2005): This is a nice survey of frictional labor market models. It covers both the basics of random search and directed search models.
QuantEcon: This is a great resource for learning more about the computational tools used in economics. There are many lessons on solving search and matching models, here is the solution to the McCall model, which is the focus of this lecture.
Generalized Method of Moments with efficient weighting. Estimating the simple search model using GMM and comparing estimates and standard errors to the MLE estimation.
Simulating data from a simple search model and simulated method of moments with efficient weithing to estimate parameters. A short discussion of other forms of indirect inference.
Duration dependence and duration estimation with Weibull hazard rate. Proportional hazard model with covariates and Mixed proportional hazard models with non-parametric estimation of mixing distribution.
Additional Material
Van den Berg (2000): Duration Models: Specification, Identification, and Multiple Durations