For cleaning your aquarium (freshwater or saltwater) a Gravel Vacuum attached to a siphon or re-circulating filter works best. If you have a planted aquarium, I recommend #00 sand (3-5 cm) mixed with laterite or conditioned soil with #3 gravel (2-3 cm) on top. You should NOT vacuum the sand, as this will tend to be sucked all the way thru the vacuum, and this will also disturb the natural aerobic and anaerobic filtration going on in the substrate being performed by the bacteria and plant roots. You can drain this water into a bucket or attach the siphon to a long hose and drain it outside or into a toilet using gravity.
There are other products that hook on to the sink, but these are over rated and waste water. It is simpler to just get a long hose and get an adapter and attach your hose to the sick to fill, but drain your water into a garden where it will do some good (unless it is saltwater of coarse).
I prefer to leave the fish in during this process, as I feel more stress is added to the fish removing them and then placing the fish back in new water conditions that the fish are not accustomed to. Add water back slowly, and if tap water is used make sure the temperature is similar to the aquarium water already present in the aquarium, you can generally safely add warm tap water to correct this. Although in the Marine aquariums I maintained, I brought my own water and it was invariably colder than the aquarium, but this does not present as much of a problem as many think. If you do some math; Say your aquarium is 78 F and you add 20% water back that is 68 F, that is 1/5th the volume, so 1/5th of a 10 F difference is only 2 F.
What is more important is adding a de-chlorinator to your tap water (if tap water is used) WHILE the water is being added. I prefer Start Right, this product removes chlorine (and the chlorine ions attached ammonia in chloramines), removes heavy metals, and very importantly naturally stimulates the slime coat in fish vs. products that drop an artificial wad of slime into the aquarium that generally sinks to the bottom anyway.

In some successful aquarium keeping traditions (especially in Germany), no vacuuming is performed. Water is simply siphoned out of the aquarium and new water is carefully added back in. For this method to be successful in fresh water aquariums, you need a healthy growth of plants, good lighting, a thin layer of sand just enough to cover plant roots (not gravel). Good aerobic filtration is also a must.

A new device that performs both water removal and recirculation thru a micron filter cartridge that is easily cleaned is the Aquarium Cleaning Machine. This new device uses a protected magnet-drive motor to remove or re-circulate your water thru a filter (or both). For saltwater changes, this device is a money saver and fish saver. You can change 20% of your water, then keep re-filtering it thru the micron cartridge using the gravel vacuum do pick up debris. This saves having to use more salt for larger water changes and keeps a healthier aquarium with lower nitrates, as much of the debris is removed from your system before it can go thru the nitrogen cycle (adding to the Nitrate levels).