Amyloodinium: Also known as simply oodinium and marine velvet disease, this flagellate protozoan causes disease most commonly in clownfish but can infect about any/every fish. Fish with the disease look slimy with cloudy eyes. They are often gilling quickly and deeply. It usually will kill the host fish within a few days which is pretty quick compared to many other common protozoan parasites and may give  a clue to the disease if you can trace the problem to a fish added within the last few days. The only way to really diagnose this disease is to identify it using a microscope. There are many other diseases which cause these symptoms and so treatments without propper identification could do more harm than good however treatment drugs do overlap with most of the other common protozoan parasites. It can be treated with 10ppm chloroquin sulfate in a quarantine aquarium for 10 days. Copper (.18ppm) and formalin (25ppm) also work but may be a bit more harsh. If you have a microscope, a skin scrape (described in diagnosing section) can be diagnostic. This parasite can be found best by taking a gill clip (can even be taken of a freshly dead fish because this parasite is obligate and it's presence alone wether on the fish or not is a problem) and seeing the small parasites attached everywhere. It will also be ina  high abundance on the external surfaces usually attached but occasionally with smaller individuals wiggling around by 1 large (and 1 small) flagella. A picture of this parasite is included here:

 Here is an excellent reference provided by IFAS.

Brooklynella: This parasite is most often opportunistic and infects fish when they are immunocompromised (stress/physical trauma). This disease I often find on skin scrapes of green chromis and butterflyfish with lesions (usually abouve and behind their pectoral fins). This can be treated with a formalin or freshwater dip or with a short (1 day) bath in copper or formalin (maybe also chloroquin). Again identification using microscopy is ideal however this bug is treated with most of the same medications used to treat the otehr common protozoan infections. I can't even find a descent fish picture of this disease that doesn't look like every other disease. Microscopically the shape of the body has a ridge along it and as theses guys swimm they look like a spiraling pringle potatoe chip. It's slightly smaller and less dense/vacuolated than uronema.

Uronema: This is an opportunistic protozoan which is often ambient in the environment and only able to infect a fish when they have open wounds or are severely immunocompromised. When there is an overabundance of the parasite becasue it has been amplified by either a sick fish or a large amount of decaying organic material in the tank, healthy fish may be so ehavily exposed to the uronema that they become infected. Fishes will develop lesions which are often red in the center and white along the margins. Microscopic identification is again the way to diagnose this bug. This parasite is pear shaped and using a higher quality microscope you can often see the cilia. Unlike brooklynellas, this protist glides quickly and bumps into things like a robot vacume cleaner vs the spiraling pong like deflections of brooklynella. Treatment in my experience is futile and the best way to avoid this disease is just maintain good water quality and minimise fish stress. You can try metronidazole or copper, in vitro research says those may work. The real tricky thing is catching the parasite before it gets systemic in a diseased fish, and this is difficult to observe. When transporting and quarantining fish, stress reducing tecniques and prophylactic dips in my opinion are the best way to mitigate this disease. Here is a link to a decent picture of this protist:

and a youtube video: (though uronema I've seen on fish are usually moving a lot faster)