I do this!! Not in India but Cambodia, Narobi and China

There are NO requirements other than you have to get your round of shots and have a passport.
Most of the time in working in the hospitals or camps you just hand out meds to the children, elderly and HIV patients. Also you help build schools and shelters. It's really whatever job they give you. There are rarely luke warm showers (usually you get a shower every 3 days.) They feed you 3 meals a day. You are given either a tent, or a hotel room. Sometimes you even stay with different families. Depends on the team you are with.
Also it's incredibly dangerous because you go to areas that aren't built up. Roads that vehicles can't travel etc, so you have to hike and walk. The buses tend to wreck. To find out how to travel safe in these areas pick up "the worlds most dangerous places" books. I highly recommend NOT going to these areas unless you've read these books.
Also, side note if you decide to do this understand you should get kidnapping insurance. Yes it exists. It does happen a lot in places like Peru and Brazil. They will post your ransom and make sure you are picked up.
Volunteer vacations is where I book through. I do NOT do anything through the red cross. (don't get me started on that rant)
Here are the sites I've used successfully.
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