Many fish illnesses are directly related to :
Injuries
Parasites
Infections
Over crowding (too many fish)
Unhealthy living conditions
These illnesses manifest themselves usually in the late fall, winter and early spring when the the fishes immune system is not fully functional.

Unfortunately, these parasites and bacteria become active around 40° F but the fishes immune system does not become active until about 65° F, leaving the fish very vulnerable to attack with no way to fight back and you must fight for him.
Treatment for a sick fish involves diagnosing the problem, then finding the suitable solution.
Success depends on how quickly you act, and how precise you are in identifying the problem and dealing with it correctly.
Koivet.com has an excellent symptom table, along with wonderful advice to keep your fish healthy.
Koicarp.net is a great source for info on koi care, as is
Keystonehatcheries.
These are also good sources for cures and pond aids, provided your fish still has time for you to shop online.
You will make mistakes and fish will die, but most will recover and thank you in their own way. If you have questions that need answering and you can not find the answers here try visiting
http://Koivet.com and posting your problem on their message board. Fish medication and consultation in Utah can be found at:
Wasatch Koior call Advanced Ponds in Sandy, 255-3698
Some more information about diseases
These first four photos from Dr. Erik Johnson of koivet.com:
To the left the photo shows a koi with probable skin cancer.

The open-mouth in the koi shown below is likely due to an abscess in the mouth but it could be something as "simple" as a foreign object caught in the mouth.

Swim bladder infections manifest themselves in many ways, but overfilling seems quite common. Sometimes the fish sinks to the bottom of the pond when the swim bladder is infected-suspect swim bladder infections if sinking fish is what you see.

A parasite infection or worm infection is usually visible- you can see something is wrong without a microscope.

Fish Concerns
Fin rot - Fins and tail appear to be rotting off, with red areas around fins. Treatment- Clean up pond water and treat with rot medicines.
Fish leach - Skin examination shows wormlike leaches. Treatment- Place fish in a container with 15 tablespoons of salt per 2 gallons of water for 20 minutes.
Fish lice - Red spots turn into ulcerations. Treatment- Give fish 30 minute bath of .1 gram potassium permanganate per 2 gallons of water. Treat the entire pond if you cannot catch all the individual fish.
Fish Pox - Pink, white or gray spots on the skin. This often occurs in spring. Treatment- General pond cleaning.
Fungus - Cottonlike growths on the skin. Treatment- Treat the entire pond. Fungus usually attacks weak fish.
Gill flukes - Parasties can cause fish to rub against objects, rapidly move their gills and gasp at the water surface. Treatment- Organic-phosphorus-based medicines, or those designed for the gills, might work. Copper-base chemicals kill any invertabrates, such as crayfish, clams and freshwater shrimp in your pond.
Gill rot - Fish appear lethargic and display red and swollen gills, mucus around gills or bleeding gills. Treatment- A slat dip of 2 tablespoons per gallon of water, or antibiotics.
Sliminess - Fins are held tight against the body and the fish rub against objects. Slimy coating can be on eyes. It is caused by too much ammonia in the water. Treatment- Test the water and treat it with water changes and medications.
Ulcerations - Res sores on the body. Treatment- Purchase a painted on medication. Also put fish into a container with 2 tablespoons of salt per gallon of water.
- Pinhead-sized white spots on the body, this is extremely contagious. Treatment- Treat the entire pond over several days to kill free-swimming parasites.
Reference: Protch, O (2008). Spring Pond Keeping.
Ponds Magazine , 8,33