Sick goldfish? New to aquariums...help!!

Question
hi there,
I bought a small non-tropical tank with filtration system, 1 live plant and a few extras and two common goldfish for my son's birthday on April 1st. The water was good when they were put in but after following misguided advice to do a partial water change every two days for the first week (and now I realise this was madness!), one fish died. The levels of amonia and nitrite were sky high, so it could have been any number of causes. I followed the advice from the pet shop to do a 50% water change and hoover the gravel and add water treatment every day and now, 10 days on, the levels are really good.
But the other fish has just started behaving strangely, hanging at the water's surface but when I come into the room, he is very aware of us (he always has been!) and starts behaving normally and swimming about. He has an appetite but I am trying not to feed too often to avoid the chemical balance being spoilt again. He appears to have small patches on his scales where it almost looks as if the colour has been 'rubbed out', if you know what I mean - I can't see spots or protruding scales or rotten fins or anything else but I am guessing that he must have some kind of skin bacterial thing going on?
What is your advice? The levels are good, and I was about to introduce a long awaited friend to the tank but am concerned about these scales etc. The tank has been getting quite a bit of sun and it's hot over here at the moment....the water feels quite tepid? could it be oxygen starvation? I have put a bag containing icecubes in the water to try and bring the temp down a bit.
Just need your advice really!!

Love Emma

Answer
Hey Emma
Actually that advice about the water changes wasn't too too bad lol.  They started out on the right track :)  When you first set up a tank, it needs to go through what's called a cycle process.  Here's a link that can explain much better then I can, should be the first article on the page, need to copy/paste to your browser:

http://freshaquarium.about.com/od/startupcycle/Step_5_The_Cycle.htm

So, when your tank goes through this cycle process, and there's fish in the tank, you'll need to do small daily water changes to dilute the toxic ammonia and nitrites in the water.  When your water parameters/levels read ammonia and nitrites 0 ppm, and nitrates under 20 ppm, your tank is cycled, and those are the parameters you want to keep the water at.  To do this, you need to do weekly water changes of about 25%, and be sure to vacuum the gravel as well.  If you don't have a test kit, I'd recommend buying one so you can check the water parameters yourself.  The dropper test kits are more accurate(and more expensive) then the test strip kits.  When there's a problem with a fish being sick or not acting right, it's usually a water quality problem, and the test kits will confirm that immediately for you-and the solution is usually going to be to do a water change.

Now, what size is the tank?  For goldfish, it's recommended to have at least 15 US gallons (about 56 L) per goldfish.  They put out a lot of ammonia naturally through their waste and breathing, and the common goldies can get over a foot long.  So if your tank is smaller then that, I wouldn't add anymore fish to it, you'll just be creating problems.

For feeding, I feed my fish once a day, and even skip one or two days during the week(I have goldies in a pond, various cichlids, community fish, puffer, etc.) he'll be fine on that kind of feeding schedule.  Feed what he'll eat in 5 minutes, and net out any uneaten food, though that's usually not a problem with goldies because they're food hogs :)  

For the scale problem, it may be ammonia burns.  The healing stage of that, they'll turn black.  Not sure if you're in the US or not, but we have a product here called MelaFix, pet stores usually carry it.  It's a natural herbal remedy that's great for injuries and healing, and some bacterial infections.  Great stuff to have on hand at home.  Another product similar to that is called PimaFix, another great one to have at home on hand, treats different bacterial infections and fungal problems.  

You said the tank gets a bit of sun, it's by a window?  If possible, I'd recommend moving it to another spot that won't get direct sunlight on it.  Otherwise you'll be getting green water from algae blooms :)  Or, if you can cover the window with a shade, blinds, curtain etc. during the times the sun comes in there.  The ice cubes in a bag is a good idea, could also try freezing some water in a small plastic soda bottle-may last a bit longer then ice cubes.  Be sure to keep up on that-changing it out when they melt, temperature fluctuations aren't very good for the fish, stresses them.  Goldies are pretty hardy fish, and can handle wide temperature variations, ideally they prefer about 68-74 F, but they'll survive higher temps and obviously lower ones.  
Warmer water does deplete the oxygen in the water, so he could be having problems with oxygen-which is why he's hanging out at the top.  You can add an airstone to the tank, and also drop the water level a bit so the filter churns the water surface more.  Surface agitation is what your looking for to allow the gas exchanges in the water.

Hope that helps, and let me know if you have more questions!!!

Christy