from https://michaelreid.typepad.com/michaelreid/2007/09/how-is-fish-oil.html 

1. raw fish enters the processing plant and is hashed (cut into pieces) and cooked by steam.

2. The cooked mass of fish is then pressed or centrifuged to separate the fat-free dry solids and the liquid (oil & water).

3. The fat-free dry solids are further processed into fish meal. Fish meal is commonly used in animal feed.

4. The liquid (oil & water) which is called press liquor is further processed to separate the oil and water.

5. The water that is separated from the oil also has solids in it and is added back into the fish meal.

6. The next stages of oil processing is calling polishing.  This is where impurities are removed via hot water.

7. The final stage of oil processing involves adding anti-oxidants before the oil is placed in stainless steel storage containers.

And other sources: