How do you prevent salmon from falling apart when frying?

Ok so you said salmon fillet. So my first question is how big is the filet. Fish don't develop protein chains to hold together the same way red meat has. So the flakes don't really hold together if pulled too hard, so I wonder if your fillets are too big. When I cook fish, especially salmon I try cut the fillet into serving sizes portions, maybe 2 inches across (assuming a full sized fish here). This helps keep the fish to a manageable size.

There is also a tool that is very aptly named because it was designed for this use and it's called a fish turner. This is a thin and springy or turner that would better with fish because when scooping up the fish it doesn't force the fish to reshape itself to the more rigid spatula and therefore you get less fish breaking apart.

Do not turn the fish too many times. Leave it on one side and let it do all the cooking on that side that it needs, flip it once and let it finish.

This will produce a nice crusty finish. As far as getting it to cook through the center, well that takes patience. Cook on a medium low heat but cook it for longer, like 8 minutes on each side (experiment, don't rely on my telling you 8 minutes). Then when you take the fish off the pan, put it on the plate and let it rest for a few more minutes. The fish will still be cooking on the inside and will finish up if you don't serve it too early, but of course don't wait so long that the fish cools. You want to serve it while it's still hot, but not scalding hot.

The best technique I've found for frying fish is not to flip it at all. I start the fish on the stove, skin down, then I finish cooking it in the oven. You need an oven safe frying pan of course, cast iron or a high-temperature non-stick works well. You get a nice crispy skin this way.

If you are set on flipping then you need to be gentle, think of it as turning over, not flipping. Get your spatula completely under the fish and lift it off the pan a bit, then putting your fingers on top of the piece roll it over, last let it gently drop onto the pan - keeping your fingers off the surface of course.

are you keeping the skin on? If you take the skin off it's likely to fall apart. If you've kept the skin and it's falling apart I suggest it's overcooked.