Looking for concrete examples of semigroups, with explicit computations done to help make the theory more understandable.

Question

I would appreciate if someone can help me find a resource which has a bunch of worked out examples showing how to find, for example, the smallest congruence containing a relation on the semi groups, and other examples on Rees morphisms, Green's equivalences, etc. They have to be on the elementary level, nothing too fancy. We're studying semigroups and I don't have a real feel for all the abstract nonsense and having examples to play with would help me understand the theory better.