Mixed-effects modeling with crossed random effects for subjects and items
R.H. Baayena, , , D.J. Davidsonb, , D.M. Bates,
doi:10.1016/j.jml.2007.12.005
Has a very clear account of testing especially the difficulties associated with obtaining p values for random effects - the 3rd author is the originator of the lmer function in the R.package
You can use the function `anova` to compare models with different random effects structures using chi-square difference tests (see attachment). By using stepwise model comparison, you can attach p-values to different changes in random effects structures.
Along with the other resources about p-values and lme4 in the other responses, see also Bates and colleagues work on trimming down maximal random effects structures: http://arxiv.org/abs/1506.04967
The issue of reporting p values from merMod objects is discussed in detail by Bates if you type ?pvalues with lme4 installed. ranef gives the conditional modes, which are estimated from the estimates for the random effect stored in merMod object. These are often described as the shrunken estimates.