Opinions vary so much on this subject that it is hard to give a reasonable answer. The Americans for instance have what is known as "Cycling", which is the period of time a tank has to remain empty of fish until the good bacteria have established themselves and are controlling the conditions of the water in the tank.
Most aquarists in the States recommend a six week waiting period using what they call "A Fishless Cycle". In order for the good bacteria to build up (starting the nitrogen cycle), they need a source of ammonia to feed on. When using this fishless cycle they recommend you add daily doses of pure ammonia to the tank for the bacteria to feed on, which is needed to actually start the nitrogen cycle working.

There is also another method used by the aquarists in the States that allows one to avoid this long waiting period. In this method the system is more in line with the methods we adopted many years ago, and it is these methods that will be mainly be concentrating on.

I would however like to point out that I personally have never used the "Fishless Cycle" method, and never shall. Having to sit and watch an empty tank for weeks on end is not my idea of a pleasurable hobby, so any references to "Cycle" in the following article shall mean the "Nitrogen Cycle", which in simple terms means the time that the system will take to establish a working biological filtration system.

To Continue.

Hopefully you have read the article on Water Conditions.
The reason you have to wait is because the water needs to become established with a good biological filtration system that only the good bacteria can provide. There are ways you can hurry this along slightly. (See Water Conditions)

Personally I find this length of waiting period unnecessary, as the work, time, and cost of the exercise would certainly drive most enthusiasts away from the hobby. I recently wrote an article, which covers most aspects of this problem, so I have placed it here for you to arrive at your own conclusions. We would set a new tank up and have it running complete with fish in about a week using the methods outlined in the Water Conditions article. In particular take note of the section that explains about using some gravel and possibly an old filter to speed the process along.

I'm probably an old 'fuddy duddy' having only been involved with fish keeping/breeding/retail/wholesale/ and supply since I was eighteen, (I'm now 62)
I've been reading just about anything of interest since I joined various tropical fish forums, and this 'Cycling' thing seems to be a major topic. This is a 'new word' in fishkeeping to me, and I suppose also to other 'non American' members. Quite honestly, "do you really need all this to start a successful hobby"

Let me, as an 'amateur' ichthyologist just run through a 'non chemical, non additive setup' that served myself and many other millions in the hobby successfully for several decades long before all these chemicals and additives became popular.

Preparation was the key, and for us 'oldies' it was a container/s in the back yard that collected clean strained rainwater. This was our source of top ups, our new water supply, and often our source of live food, if the mossie larva or daphnia got into it.
We would set the tank up, fit the u/g filter, and then arrange the pre-washed gravel. Next we would fill the tank with our pre-aged water from our rain tub, bring it up to the right temperature, let it stand a few days, normally three to ensure the heat was constant and there were no probs. In those three days we would arrange plants and rocks, then perhaps introduce a guppy or two. The old pH testing strips from the chemist gave us a quick idea of the pH level, and if it was alkaline we would run a bit of peat in the filter bowl for a day or so to bring the level right. If it was too soft and acid we would add a bit of limestone or coral chips to the box filter and keep an eye on the pH until it was where we wanted it. Basically that was it, with little or no stress to the fish. Our calculation for fish content was to allow 4sq inches of surface area per inch of fish, but with an air supply this could be increased. Water was never added unless it was exactly the same temperature as the water in the tank, and newcomers were never added until they were quarantined for ten days. Plants were meticulously examined for nasties and rinsed in a mild sterilizing solution before adding to the tank. All mainly common sense.

Each tank had it own net and tools, and nothing was ever taken from one to the other. Dipping of fingers or hands from one tank to the other was an absolute sin, and never done. Hands were washed before working on the next tank, and any drips or condensation were wiped away in case it/they dropped from one tank to the next lower one. A single drop of water can transmit a disease from one tank to another so quickly you wouldn't believe. Water changes, (In my case) were done on a visual basis. If the water has evaporated ½" from its original marked level I would do a 30% water change, never every few days, and never more than perhaps once a month, and always using my aged water in the outside tub/s. Invariably the tanks might have needed a clean up, so in this situation we would siphon the rubbish off the bottom and into a bucket. The water that we siphoned out was dumped and replaced by our aged water. This was then our "water change" and few troubles were encountered.
A balanced tank will keep itself free from excess toxins,
Eg, the right water conditions, substrate-plants-filtration-and fish, any of which can cause an unbalance.

Water:
Too hard, too soft, too alkaline, too acid, all of which can be balanced without chemicals. (See Water Conditions)

Substrate…. Gravel:
Too fine, (packs down tight) causing bad circulation, especially with u/g filters, whereas too large a gravel will allow food to reach inaccessible places with dire consequences. Food remains uneaten and quickly fouls the tank. Remedy, go for what's right, not what looks pretty.

Slow deterioration of Rocks and Ornaments
Badly selected rocks and substrates, (lime-based gravels, sandstone's, corals, shells, ornaments,) all of which will change your tank conditions as they slowly leach or dissolve over time. That ornament or substrate may look great, but is it killing your fish?

Plants:
Too few plants, no hiding places for fragile fish causing fish to be bullied. Again, find out the likes and dislikes of your plants, for instance, most Crypts prefer dimly lit areas, etc. Shallow gravel will not produce good plants. Bank your gravel to the rear of the tank (at least 3") and plant accordingly, big deep rooted plants to the rear, small types to the front. As with your garden, they need feeding and something to get their roots into. The wastes from your fish may in most cases be enough food, but a good root structure and light are essentials for all plants. A 'Plantab' for aquarium plants slipped under the roots will assist flagging plants.

Filtration:
NEVER turn your filter or air off for any length of time, especially an undergravel filter. The bacteria buildup will skyrocket causing major probs instantly. Always have some form of air supply running if your tank is in the least bit crowded.
Contrary to belief, the bubbles from an airstone don't put oxygen in the water. What the bubbles do is break up and disperse the CO2 that can build up in a tank.
Watch for fish lurking near the surface with open mouths, a sure sign of lack of oxygen in the water. (Not the Gouramie's, Betta's etc, who/which are surface breathers) For these fish ensure the surface is scum free by dragging a sheet of paper over the surface of the water occasionally. This will completely remove the thin film that sometimes forms on the surface of the water. Check each day.

Heat Distribution:
Fit your heater as low as possible in your tank and clear of the gravel, and if it is a separate unit from the thermostat place it at the opposite end of the tank. This will prevent cold spots in your tank and provide a constant temperature at all levels. (Heat rises, so if possible fix your heater horizontal rather than vertical position for better heat distribution)

Feeding:
Feed half as much as you think your fish need, and if its not consumed in less than five minutes, you are feeding too much. An established tank will sustain your fish for a week or more without food, so don't think you need to feed them every time you pass the tank. "Ooh look, they're all excited at seeing me, they must be hungry…"
In goes another feed, the third today. How often have you done or said this.

When to feed

Never feed at night then turn the lights off and leave the fish in darkness, a major problem. The cory's and Kuhli's won't mind, but your tank will suffer if the night dwellers don't eat all the remains of the food.
Small fish have small mouths, so vary your food type to suit them all. Give them a live food treat now and again, brine shrimp, micro worms, grindal worms, white worms, or even a chopped up earth worm if you have big fish. In time you will know their likes and dislikes.

Probs with algae, throw the scraper away an get a couple of small Pleco's. They're fun, hardy, and adore algae. Snails… To me they are a damn nuisance, and have no place in a tropical fish tank, but the fish love them if you crunch them up.

Impulse buying of fish is fine if you know the fish, and of course is great for the LFS, (Local fish shop) but can cause many upsets and even tears if you don't read first, so take an hour or so and read all you can before you jump in the deep end.

Lastly Fish:

Read, read, read, The three rules of keeping fish. Learn every possible thing you can about where your fish comes from, its water conditions, its temperature limitations, the food it eats, the species it can live with, its breeding habits, is it a loner or does it school with others, and in general, its likes and dislikes.
Piranha's and Neons have an adipose fin, and are distant relatives, but they definitely don't live together, so read and learn all you can BEFORE you add that particular fish to your collection. (No comments on the Piranha's please)

It seems a lot to take in all at once, but all this info is on this siteand many others just waiting to be read if you care to read and study it.
My philosophy is that "If anyone can teach me something I will listen, should it be a child, or a ninety year old," so I am learning each time I read an article about tropical fish.

We all lose fish at some time or other, and the reasons can be mystifying, but personally I feel that many of the losses are caused by either sheer neglect and not making ones self familiar with the fish BEFORE purchase, along with the possibility that many of the fish were actually poisoned due to the intake of chemicals, incorrect or too many water changes and such.

We can take a pill for a headache or an ailment, but if we take too many of them it will undoubtedly kill us. This will possibly cause a lot of backfire from the clued up aquarists, but I still feel that if you read up on your fish, get to know its habits and living and water conditions and the neighbours it lives with, then you are well on the way to having a less stressful and very enjoyable hobby. Many newcomers try it once and leave quickly after their first failures. We don't want this to happen to you, so read everything you can about the hobby, consider your situation and your setup, then, and only then think (very carefully) about your next purchase.

Just a note for people who keep goldfish in a heated aquarium.
All fish have the right to a decent life, even goldfish.
I myself have culled thousands of fish in my time I suppose, but these were either runts or a defective strain that I would not allow to continue living and breeding for fear they would fill our tanks with some of the oddities I see today.
Selective breed by all means, but don't allow your runts and defective breeds to enter the world of the aquarist. (Are there any 'true' strains still out there?)
Goldfish in many cases are cold water fish, and keeping them at 80+ degrees will shorten their lifespan by many years. We had goldfish that lived happily for ten years, outside in a pool that would freeze over in winter with over an inch of ice, but come spring they were always there. The heated tank may also cause undue stress to the fish, who knows. Why not be a good aquarist and introduce some youngster to the hobby by donating your fish to them rather than make the fish suffer all it's life, but make sure they read a good book about goldfish first.

There are exeptions here of course, and the ornate varieties do need the warmer temperatures, (never over 80degF) so if you follow the easy rule "The fancier the variety, the warmer the water it needs", you will see that your common goldie may be happy in an unheated tank, but your fancy Moor or Veiltail might not be. (See Coldwater Section)