Simple Bisimulation algorithm
The coarsest bisimulation has a well known greatest fixed point characterisation. This greatest fixed point characterisation gives you a simple algorithm to calculate bisimulation quotients. There are quite a few immediate improvements you can make to this algorithm. A reference that contains most of these details is Joost Pieter Katoen's lecture on bisimulation minimization. If you need more detail, I suggest looking at the book


  Principles of Model Checking, Christel Baier and Joost-Pieter Katoen.