[just  a few of the more popular problems]
Ichthyophtirius:  This looks like someone took a salt shaker to your fish. "Ich" is usually a sign of stress and can wipe out your tank quickly if gone untreated. When we see it with the naked eye, the parasite is in it's shell form and is hard to treat.Treatment begins immediately even though the parasite cannot be killed until it breaks open and becomes free swimming.A treatment of formaldehyde and malachite green {something like "Quick Cure"}  works very well but if you have clear silicone edges on your aquarium, it will stain them green. Read instructions carefully before administering doses. Some tetra and exotic plecos cannot handle a full dose. Raising the temperature in the aquarium by 2 degrees F per hour to 86 dregrees F for 10 days will also speed up the life cycle and send it into dormancy.
Just like us when we are sick, fish like to be kept warm in a aquarium with low lighting. Make sure there is enough oxygen in the aquarium.  Remember, the higher the temperature the less oxygen there is .
Bacterial Fin Rot: A fuzzy deteriation with possible redness eating away at the fins.
Septicemia:This shows up as red streaks usually on the fins, but can also be seen as red patches on the body.

Water Quality is one of the biggest factors in disease prevention. Doing regular water changes with a good vacuum greatly decreases your chances of getting any of the following conditions. Doing a few water changes in a row usually clears up fraying fins.
Dropsy: Lifted scales on fish. This will make your fish look like a pinecone.
Bacterial Infections: This looks like gray patches on your fish. Sometimes fungus can grow on top of these areas.
Fungal Infections: This can start by an open wound, whether it be a bite mark, bacterial infection, or a scrape from a rock during an aggressive display. This is a white fuzzy clump of cotton.
These  conditions described above can all be treated with Kanamycin and/or nitrofurazone. Erythromycin is also very good. Look for broad spectrum antibiotic medications at your local aquarium store.  Melafix (which can be mixed with salt) is a good remedy on fin rot and open wounds and can be much cheaper than antibiotics. Coppersafe can be used with Kanamycin and Erythromycin.

Velvet: This condition is less likely to be diagnosed by a beginner. It looks like someone has pored sleeping dust over your entire fish. This is easily treated with copper sulphate (coppersafe) or even better, Ionic copper (Cupramine) 
Copper sulphate (coppersafe) and ionic copper (Cupramine) can be used for many parasitic conditions but should be used carefully. If any kind of unusual behavior should occur, add fresh carbon and do an immediate water change.
Swim Bladder Problems: In Orandas and fat bodied gold fish, you are probably only feeding floating pellets or flake food. These fish need sinking food so they will eat off the bottem and not fill up with air while gulping food at the top. Flakes can still be given if you sink them first. Other fish may have problems with their bladder if they do not get enough vegetation in their diet.