I've lived in India for almost five years now, and I believe it's better to err on the side of caution here. For drinking water, stay away from all fountains, taps and the like. I would stick to this advice even in the airport and at hotels. Also use bottled water for brushing your teeth.
Buy bottled water of a known brand. (Bisleri, Aquafina, Kinley.) It's preferable to get them from a large supermarket or other trusted source, to avoid counterfeit bottles. Your hotel will probably sell them. Make sure the caps are sealed. You can typically get 5L or even 10L bottles. If you do this, though, make sure you don't get the type where the same bottles are reused, as the refilling process can often be unhygenic. Below is a picture of reusable bottles that you want to avoid. They feature quite sturdy plastic. These are 20L, but smaller varieties and shapes also exist.
If they ask for a deposit on the bottle, and the bottle is exchanged back for another bottle after use, then you know you're dealing with reusable bottles. Some of my friends have had water tests done of the reusable bottles (of a known brand) and found that they are more likely to contain various bacteria. The tests of the disposable bottles, on the other hand, turned out fine. If there is no deposit on the bottle, then you know that each bottle is new.
Stay away from reusable bottles, even from known brands. Any local refilling facility may or may not have their procedures in place.
Here is an example of a disposable bottle (which is what you do want) from a trusted brand:
This bottled water is quite cheap here. A 1L bottle costs €0.26. A 5L bottle costs €0.87.
Personally, I have my own RO system, UV filter and ozonizer, but that's usually not an option for short-term visitors.
Since most of the bottled water here is RO processed, it's good to choose a type that has added minerals in it (Bisleri, Kinley). The RO process removes all bacteria and harmful chemicals from the water, but it also removes all the useful minerals.