Actually a lot depends on the type of tank you have. I will give details for two common types. The small fish bowl and the small aquarium tank.
Fish Bowl.

Using a fish net, carefully catch the fish and place in another bowl or clean container that has never been washed by soap. Rinse the tank well and be sure to get the debris out of the gravel, etc. Add room temp water and a dechlorinator and reintroduce fish.

While fish bowls are effective for a Betta, it is actually a very bad idea to keep other fish, especially goldfish in a fish bowl. They need much more space and water oxygenation.

A small aquarium should not have to be completely changed. Each week, you should be able to remove 20 to 40% of the volume and replace with fresh clean water. There are many easy to use siphons with gravel cleaning attachments. These are excellent for removing debris from the gravel and siphoning water into a sink or bucket. Once you have remove a portion of the water, rinse your bucket well and refill with treated water at room temperature or as close to the tank temp as possible. It is important to use dechlorinated water as many cities use chlorine and chloramine to treat water and this is toxic to fish.

NEVER use soap on aquariums. Soaps leave residue that is toxic to fish. Often the phospahtes and the detergents added to cleansers will cause distress and even death in fish. Use warm water and if you need to scrub, add salt as a scouring agent and rinse very well.

Partial water changes are best for any aquarium, as it does not disturb the bacterial balance the tanks needs to do well, and it removes many of the biological waste products that build up. A total tear down of any tank larger than 5 gallons is not advised and you should do partial water changes.

Have you looked at WikiHow? Here is what they say: 

1. Make sure you have everything you need! Run through your checklist, and make sure everything you need is within reach.
2. Start the siphon and direct the water into a 5-gallon pail. You may need a larger bucket if you have a large aquarium.
3. Push the gravel vacuum through your gravel. Fish waste, excess food, and other debris will be sucked out through the vacuum.
4. If you have a sand substrate, do not use the vacuum like a shovel. Use just the hose part of the siphon, not the plastic tube, holding it under an inch from the surface to suck up waste without disturbing your sand.
5. If your decorations are covered in algae, you may want to feed your fish less or change the water more frequently. Excess algae growth is caused by excess nutrients in the water. You can wipe the decorations off in the tank water you siphoned out, and use an algae scrubber to remove algae from the walls of the tank.
6. Don't change the filter cartridge unless it is falling apart. The filter is where a lot of the beneficial bacteria in your tank lives, and replacing the cartridge will kill the bacteria and cause toxins to build up in your tank. Instead, you can rinse it in the old tank water to clean it off every once in a while.
7. Replace the water you took out with fresh, treated water at the temp of the aquarium.
8. Any cloudiness that remains will normally dissipate in a few hours, leaving the water sparkling clear.

From Video Jug: This film will show you the basics of keeping your fish tank clean and healthy, including cleaning the aquarium filter and the gravel. (I'm not sure if the video will embed, don't know why I can't see it...please be patient to go to the link).