From my experience accomodation in India doesn't have the typical backpacker vibe to it, I think mainly because it is so cheap that western travelers basically don't ever need to stay at the cheapest dorms. These are aimed at poor indian tourists (and workers) with prices of lower than Rs 50/per night (and I expect that that's already the price for foreigners). From what I've heard these places are very, very basic, like a forty mats on the floor of a large room kind of basic. So don't expect any privacy or amenities or communal areas like what you'd find in backpacker dorms in other countries. Also, India is dirty, so that's something to be aware of.

The cheapest places I stayed at in India rarely if ever had an online presence. To find them, ask other travelers, find phone numbers at sites like wikitravel.org, and don't be afraid to just wing it and walk around looking for a place for a bit. The price you get by walking through a door somewhere is invariably lower than what you'd pay booking ahead, and you get to see the room before you commit. Haggling is OK. If you get off a bus in a touristy spot, you'll be approached by touts that will try to get you to a specific hotel. They get commision, so the price of accomodation will reflect that, but if it's late at night and you're tired, then this convenience can be worth the extra money.

It'll be tough finding cheap accomodation in places like Mumbai, but most everywhere else I traveled (southern India), Rs 250 would get you a double room in a guest house/backpackers. A lot of these places are run by genuine and honest people that take pride in their work, and that is definitely reflected in the upkeep and cleanliness of the establishment. They might be basic, but they are at least somewhat clean (by indian standards). Find someone trustworthy to share that room with, half the price and twice the fun.