On the second day after I arrived in Delhi, I managed to get a SIM card. This was fairly straightforward: I only needed a photocopy of my passport and two passport-sized photos (the store took them for me), and the address where I live (in India). Just in case you didn't know, I don't live in India. So, I had planned to get AirTel, but the owner of the little hole-in-the-wall shop advised me that I'd be better off with iDEA, because AirTel attempts to verify your address a week after you purchase a SIM. Since I'm not staying at any hotel for more than a couple days, that might be a problem. I guess IDEA doesn't do that. Dunno. In any case, I got a SIM card for Rs 99, and paid Rs 500 for Rs 350 worth of "talk time".
I was advised that I could get a Rs 20 / day unlimited data plan if I called customer service, and I left. Later that night I attempted to call customer service. Unfortunately, this was an automated menu system, with prompts only in Hindi.
Now mind you, the packet the SIM card came with is bilingual: English and Hindi. The page telling me what number to dial to reach customer service was in English. Every representative I ended up talking to spoke English to some degree or other. But the menu system was only in Hindi. One of the people I'm traveling with speaks a bit of Hindi, so I wasn't even totally helpless. But even so, we had a lot of trouble figuring out the proper menu choices. So the first representative we spoke to said that it was the wrong department (I think it was the postpaid customer support), and when we enquired how to access the correct people, since the Hindi was somewhat of an issue, he said "oh you just press 1 for English in the menu" and hung up. Which was false. Eventually, I managed 1-1-9 to get to a human who didn't hang up. Success! And it turned out I just had to SMS "ACTNET20" to 12345. What he didn't tell me was that it would take a day and a half to go through. Wasted about Rs150 on non-unlimited data before that actually went through. Oh well.