While there is still a ton about fish disease we do not understand, it is possible using a few simple tools to identify some of the more common disease causing organisms. Remember that not finding external parasites does not rule them out entirely.
Before acting on impulse and medicating or performing some other drastic change to your aquarium, consider what might have caused the problem. Think about new fish added, fish aggression/food competition, diet (recent change or you only feed a 3 year old flake food that has been sitting in the windowsill and has lost most nutrients) , potential toxins that may have gotten into the water (bug spray/hairspray/new equipment), and above all else, water quality. Get the relevant water test kits (see starting an aquarium section). It is so common that people allow quality to slip and then wonder why their fish get sick. Crappy water quality immunocompromises fish and often concentrates opportunistic pathogens (especially bacteria but also some protozoans like Uronema). Fix that first.
There are a few simple techniques that can help you diagnose the pathogen correctly so you can treat appropriately. When parasites cause disease in fish, they are usually in a high enough abundance to isolate from the skin/fins of fish using a microscope slide cover slip and scraping along the surface. Then, mounting the cover slip on a slide and looking under even a low quality low power lense, metazoan and protist parasites are often diagnosable (just look for microscopic pictures on the net for the various worms/crustaceans/protozoans for comparison). Another trick, if there are just a few large parasites or you suspect clear parasites or bugs in the gills, is to do a freshwater dip in a clear container and see what falls off. Neobenedinia, a flatworm that often clouds the eyes of fish, look like rice grains when they fall off in a fresh water dip. If you don't find anything and the entire body of the fish is affected, start to think about nutritional/toxic/bacterial disease. I've left viral out because, while maybe they are rare (we don't actually know though as tracing cause of death to them involves molecular techniques), you often can't treat those anyway (exception is lyphocystis).
Theres no silver bullet to curing all fish disease and treating incorrectly can cause further problems.