Not all aquarists use tapwater in their aquariums; some use rainwater, whilst others prepare pure water using reverse osmosis units. But in general the cheapest and easiest method is to take water straight from the tap and prepare it for use by following a few simple steps. This is usually very effective for all but the most fussy species.
What's wrong with tapwater? Although tapwater is good for humans to drink, it is not suitable for fish. Adding either chlorine or chloramine disinfects the water, eradicating bacteria that would otherwise multiply in the pipes, and cause outbreaks of diseases such as Cholera. But these chemicals are not good for fish, causing gill damage and ultimately death in most aquarium species. Furthermore tapwater is generally too cool for immediate aquarium use. Some very hardy species (such as goldfish) may survive the ordeal of being kept in untreated tapwater, but they will certainly not thrive, and will most likely suffer to some extent.
Chrlorine and chloramine: Chlorine will slowly dissipate from tapwater, and simply leaving it to stand for a few days will generally be sufficient treatment. Aeration will speed this process. On the occassions that water companies use chloramine (this may even be just for a week or two each year) aging the water alone will not work. Unfortunately it is impossible to know how the water has been treated, so a drop or two of a commercial dechlorinator really is the best way to condition water for the aquarium. They neautralize chlorine making it safe for aquarium use in just a few minutes. But do read the label, as a few lesser brands remove chlorine but not chloramine.
Temperature: Tap water is generally much cooler than aquarium water. Adding cold water will often shock fish, making them more susceptible to disease, and so should generally be avoided. This is not always the case; sometimes the addition of cooler water can induce fish to spawn, but in most situations water added to the aquarium should be the same temperature as the tank water it is replacing. A well-kept aquarium will have regular small water changes. In this case a small temperature difference will make very little difference.
Anything else? In some instances, tap water may be too hard, too soft, or even too full of other chemicals (nitrates, for example) to sucessfully keep certain species; in these cases it might be worth considering only keeping really hardy species (usually the least expensive!), and the fish that are suited to your local conditions, rather than struggling with fish that would never experience them in the wild.
In short, the best regimen for using tapwater is (i) to change small amounts at a time, (ii) to remove chlorine/chloramine with a good dechlorinator, (iii) to ensure the replacement water temperature is close to that of the tank, (iv) get to know your local water (ask at your local aquarium shop if you are not sure) and if it is extreme stick to species that suit.