cycling your tank - the most important step
All new tanks need to cycle biologically before they are safe for fish to inhabit. When fish are kept and fed in an aquarium, all their body wastes (and any uneaten food) are simply dumped into the water around them. This results in a buildup of ammonia, which is poisonous to fish, in the water. Luckily, there are strains of bacteria (called "Nitrosomonas") present everywhere that are able to “eat” the ammonia as nutrition, and in turn produce less-toxic nitrites as wastes. It gets even better though, because there are yet other species of common bacteria (called "Nitrospira") which consume the nitrites and produce nitrates, which are far, far less toxic to fish than nitrites or ammonia are.
A cycled tank has invisible colonies of both ammonia-eating and nitrite-eating bacteria well-established in the tank, which easily neutralize the wastes in the water so that the detectable levels of ammonia and nitrites are basically zero. However, in a fresh tank, ammonia builds-up and spikes rather high before the ammonia-eaters grow plentiful enough to begin to drive it back down. As this happens, nitrite levels climb and then they spike and begin to fall as the nitrite-eaters become plentiful. This usually takes 4 to 8 weeks before ammonia and nitrites fall to zero, and then the tank can be said to have cycled.
Failure to cycle properly is why many new fish keepers end-up with a tank full of dead fish 2-5 weeks after buying them, a phenomenon that is so common that it has its own name: new tank syndrome.
Use hardy fish to cycle your tank
When a tank is cycling, ammonia and nitrites build to poisonous levels. For a while, life is hell on the fish you have in there - gill damage, eye inflammation, and many nasty processes are being visited on the fish. Some fish are able to withstand the toxic spikes, and others will just perish. It is often the fish that have been bred in aquariums for generations that tend to handle these spikes best. Tetras and Platies are especially hardy. Even if you want more delicate fish, it is best to cycle your tank with these "starter" fish and then return them to your fishstore. Most will happily do this. For instance, many local fishstores will routinely sell Tetras for $3 and buy them back for $1.
Never use more than two or three fish to cycle your tank
Even with hardy fish, there is only so much toxicity they can take before they are seriously injured and die. Given that the ammonia and nitrite consuming bacteria will take 4-8 weeks to grow to beneficial levels, if your ammonia and nitrites accumulate too fast for the small bacterial population to process, the water will become very toxic very fast. Having more than 2 or 3 fish in the tank during the cycling process will usually cause this to happen. What you end-up with is dead fish and a tank that has not completed cycling, leaving you at square one.
Do not allow ammonia or nitrites to rise above certain levels
Use a test kit to monitor ammonia and nitrite levels every 12 hours during cycling. If ammonia rises above 5ppm (parts per million) or nitrites rise above 3ppm, do a 20% water change to bring the levels down. Remember to use the water conditioner. Do water changes every 6-12 hours if necessary to get them below those limits. It is not advisable to change more than 50% of the water at one go as that can lead to shock or stress in the fish.
Seed your tank with good bacteria
Your tank will cycle more quickly if you borrow gravel from an established disease-free tank. Sometimes you can offer to buy this from your local fishstore. You can also buy a Bio Spira packet (made by Marineland) and pour it into your tank. The Bio Spira should have been refrigerated. If it is sitting on a shelf before you buy it, the bacteria in it are mostly dead and useless.
Consider fishless cycling
Even with all due precautions, cycling takes away some of the lifespan of your starter fish. Research in the past decade has now made it possible to cycle fishlessly. Of course, that means you are maintaining a tank that has no fish in it, so it is delaying that gratification by upto two months. However, fishless cycling is simply the most humane way to cycle your tank. Read more about it here.