How do I stop fresh fish from falling apart while cooking?

I would suggest cooking them in a pasta strainer.

This way you could pull the strainer away from the water and drain the fish in the strainer. Then pour the fish out of the strainer in one piece instead of trying to lift the fish out of the water.

Something like this is useful:

Photo source

There are a lot of variations on the same theme (including oval strainers)

My first thought is to cook the trout less time. When the fish is just done, it will not fall of the spine (I think).

Another option is to change the cooking method. I sauté'd a fresh trout (the neighbor had caught it) with good result.

Fish is delicate. So boiling it (you don't say how long for) for more than even a minute or two is going to cause it to disintegrate. How about cooking it a different way?

The best way to cook fresh fish is to put it into a plastic bag with as little air as possible (there are vacuum sealers available for that, but manually squeezing air out of the bag should work too), and place it in a water bath.

The plastic bag is necessary to prevent water access to fish while cooking. You need to keep temperature of that water at 132 Fahrenheit (55.5 Celsius), not less, not more (at 145F it'll already be overcooked). Depending on how thick is the piece it might take from ~20 minutes (half-inch thick) to couple hours (~2 inches thick) to make sure the entire piece was brought to this temperature (especially important if starting with not fresh, but frozen fish). After that you could just fry it for 30 seconds on each side to give it familiar "fried" (or use a propane torch from Home Depot) slightly "brown" look.

If you don't want to mess with plastic bags and keeping water temperature precise, still using a digital thermometer with a needle type sensor will help a lot in any cooking. The "doneness" of fish (and meat) depends only on what temperature you brought it during the process.

If currently you're simmering it — temperature is way above 132. It's most likely close to 220. Means — severely overcooked.

I had the same problem. Don't move the fish until its done on one side before flipping. then it will not fall apart.

I am from the Bahamas and the way we keep fresh fish from falling apart is this:

After seasoning the fish, take a clean hand towel and gently tap the water off the fish until it's damp but not dry and be careful not to rub off the seasoning. Take a flat plate, sprinkle some flour on it and spread the flour to ensure it coats the entire plate. Take the damp fish by the tail and dip both sides of the fish in the plate of flour. Make sure the fish is lightly coated from head to tail.

Use a skillet filled with approximately 1/2 cup of oil and fry the coated fish on medium heat.
When you notice the fish is slightly brown, turn the heat up and fry to a crisp golden brown. Add oil only as needed, too much oil will soften the fish and too little will cause it to stick. Watch the pot carefully and use a spatula to flip the fish. When flipping, make sure the spatula is in between the head and the body section.

This method is done before we cook the fish in any other form to prevent it falling apart. This is especially done before the fish is steamed, because it decreases the cooking time of the fish sitting in gravy, which causes it to fall apart if cooked for a long period of time.

i use the two spatula method. one goes under the fish and one goes over. the one that goes over the fish is "face down", so I can even turn it without it falling apart.