I personally believe that there are 3 ways to have water that is as transparent as air.. as if it's not there.
In addition to what JanS said:
1. One must ensure that the bacteria works at their best.
That means a lot of Oxygen in the water. Yes Oxygen, not CO2
To me the best way to add Oxygen is to make the plants produce it. Which means CO2 and proper fertilizing.
2. Use of fine filter pads in the filter.
If it is feasable - a micron filter. Magnum HOB or a unit that is connected inline with the canister filter so the coarser debries don't clog the micron cartridge in 2-3 days.
A sterilizer breaks up everything that is floating in the water. Microscopic floating particles (algae, debries) make the water appear less than totally clear. A sterilizer has a very small "polishing" effect on the water but it's effect is not to be underestimated.
Use filter floss in your canister filter, those sponges don't remove as many small things as filter floss, as well as water changes, clean glass, and cycling. Plus glass has a hue to it, you can get better tanks that have clearer glass. Acrilic also looks clearer than normal glass. If you doubt me look at the seam of your tank down the planel sidewase and you will see a green milkey hue.
My 10 gallon apears so crystal clear as though the plants are supporting themselves. It's a 'plant farm' and 'shrimp farm' with no wood or anything that would leach color. I'll probably scape it at some point though. I've heard that UV sterilizers are a no no for aquariums since they also kill benefitial bacteria. I might be mistaken though.
At this tank I have installed only 1 Eheim canister filter (I think a 2324 Thermo version). No UV-Lamp install. After the filter there was a CO² reactor from AquaMedic, before the water goes in the tank.
My goal at this tank was to hidden the most technic. The inflow was hidden under the stones, and the out flow comes out between the stones and the Heminathus. I was like a water spring coming from the bottom. It was hard to see it...but this is what I want
At the bottom of the tank was installed 2 drill hole fot the in- and outflow.
The reason why is water so clear ? Maybe because I visit this tank since view weeks every 3-4days...then I change about 60-80 Liter. At every visit.