It will depend on where the ...

It will depend on where the water is being discharged to.  However, almost without exception, the first stage will be a balance tank to help even flows, and dilute any pH effects involved in cleaning.  If the process is poultry, then the first stage should be screening to remove feathers and then flowing to the balance tank.  From the balance tank, the water should be sent to a DAF plant.  There are two choices.  Either the water should be put into mixing chambers with stirrers to correct the pH, to dose coagulant and then polymer, or a series of pipes doubling back on themselves producing turbulent flow where the pH can be corrected, the coagulant dosed and the final polymer dosed.  This all occurs before the DAF plant.  The DAF needs to be sized for a constant flow.  With the correct pH, the correct coagulant and polymer, fats and small solids are separated using air and a scraper and beach system.  The fats removed can be rendered providing the coagulants and polymers are chosen correctly.  There will be significant BOD/COD levels flowing from the DAF plant including ammonia levels.  If there is a municipal treatment works, which will accept these then well and good.  If not further treatment will be required.  In that case the lowest cost is some form of aeration preferably fine-bubble aeration with good mixing.  Ideally a small anoxic zone where returned sludge is mixed with fresh liquor before going to the aeration tank where aerobic digestion occurs.  The mixed liquors are sent to a settlement tank big enough to separate the sludge from the clear water.  With the correct design, this water can be good enough to discharge into a water course.  As a more expensive option, a membrane system can be used instead of a settlement tank.  This is more costly to run and cleaning is required of the membranes, also there is a cost attached to membrane replacement.  The alternative to aeration, is the use of anaerobic digestion.  This is more complex and you may still have levels of phosphate and ammonia to dispose of, but the end product is methane, which can be used to produce heat or steam for the plant.  Even this isn't that simple and although it looks good on paper, a number of smaller AD plants have been removed due to the difficulties running them.