There's a little Airtel shop just as you exit customs that sells prepaid SIMs. You need your passport (unlikely to be a problem as you're coming from immigration anyway), they'll snap a digital pic and then fill out vast amounts of paperwork just to give you that "welcome to Indian bureaucracy" feeling. Cost is a little over Rs 500 including some talk time and the whole thing shouldn't take more than 10 minutes.

Activation times are entirely random. Sometimes they work off the bat, sometimes it takes a couple of days and you have to yell at customer service until it starts working.