In a fish pan or skillet, simmer the chopped celery, onions, and carrot on medium-low heat in lightly salted the water, for 20 minutes to a half hour before adding the fish.
Add the whole fish (gutted, scaled and cleaned) into the pan along with the vegetables. The fish will be done when its eyes pop out, its skin parts when touched, and its flesh becomes tender; in terms of cooking time figure 10 minutes per inch of thickness of the fish, measured at its thickest point. Turn it, carefully, when it's half done, and leave it in its broth until you're ready to serve it (the broth will be quite tasty, and if you strain it, will be perfect for making Lenten Cabbage Soup).
Rubbing the fish's skin with a slice of lemon will help keep it intact.
A good boiled fish will do very well served hot, garnished with fresh parsley and accompanied by freshly made mayonnaise or some other sauce, and a vegetable.