It's important to understand that in most cases, fish that exhibit symptoms are very ill, and so it is normally important to act quickly.  Nearly every illness can be attributed to one (or more) of 5 things:

I am often asked what fish are good for beginners, and that can be a tough question to answer, since there are a lot of variables like tank size, and whatnot.  Goldfish tend to be the common starter fish, but an understand of the physiology of goldfish will lead you to realize that they are best left for large ponds, in the long run.
 
Below are a list of fish that are commonly available, typically healthy and are robust enough for beginners:

Early in my fishkeeping days, after I had killed many a fish due to ignorance about the nitrogen cycle, I was quite frustrated by my inability to keep new fish alive, particularly the more delicate fish like Angels and Rams, but also common fish like dwarf gouramis, mollies and swordtails.  Like most, I was buying my fish from the local Petsmart and Petco's, bringing them home, floating the bag, adding a bit of water, then letting them loose.  Within a few days, the fish would start developing sores or just outright die.