Note: if your stay in India is less than 3 days, forget getting a pre-paid sim
Thankfully, I did some research beforehand and had some idea of the process. Unlike in most countries where you can get the sim activated on the day of purchase, it actually takes days (2-3 days to be more precise). You will have to call a certain number once you get signal to verify your name, address and father's name. I would assume these safeguards are in place for reasons relating to terrorism. Otherwise, it would simply be appalling inefficiency.
I chose
Airtel (Red logo, you won't miss it - right when you enter the arrival hall at Delhi International Airport), in part for its affiliation to Singtel (no, I am not a shareholder at the time of posting), although Vodafone would probably serve the same purpose. Again, another complex process awaits; a form to fill, affix a passport photo (don't worry if you have used your last for your Visa on Arrival; they have a webcam and color printer to serve as a crude backup).
I was carrying an iPhone 5, so the guy had to cut the sim into nano sized (I'm pretty sure he has a micro cutter if your phone requires).
In all, I paid about S$10 for 200 minutes worth of local calls and 1GB of data (valid for a month). Data allowance and credits could be used anywhere in India (I visited a few states). The salesman tried to peddle a top-up of 1300Rs (S$26); but I knew better. Ask for the cheapest top-up amount with data, you can top-up if you run out of credits.
My advice is, if you are staying for more than 1 week, get the data. Against conventional wisdom, Google Maps actually work wonders in India (especially if your tuk-tuk/auto driver has no idea where your hotel is).