Its really dependant on the type of tank you have, there are a few types, but we will discuss the most common ones. The two most common are the small aquarium and the simple fish bowl.
***Fish Bowl***
Carefully remove the fish, and put him/her in a seperate container. Run the bowl under water and be certain to get the garbage and such out of the rocks. Fill with room temperature water, add vitamins and dechlorinator. In 30 minutes let the fish go back to his/her home.
Goldfish actually do poorly in a bowl. They need more room, and more air. Siamese fighting fish do well in this environment however.
***Small Aquarium***
Aquariums should not get completely emptied. Weekly you should change 20-30% of the total water and simply replace it with clean water. If you get a siphon tool with a gravel cleaner you have a very simple and efficient way to keep your tank clean. Remember to use dechlorinated water!
Also soap in aquariums is a big NONO. If you must scrub, use salt.
Remember use partial water changes to keep your fish healthy and happy.