Where + who
At every major arrival airport there's an Airtel + Jio counter airside (post-immigration). Airtel is the safer bet for coverage in less-touristed states; Jio for 5G data in the metros. Vodafone-Idea (Vi) is the third option; skip it as a foreigner — the paperwork is longer.
What you need
Passport, visa page photocopy, one passport photo (a spare from the visa application works), an India address (your hotel is fine), and a local reference (the airport counter often waives this or uses their own).
Plan choice
Grab a Rs 500-Rs 800 (~£5-£8) 28-day plan with ~2 GB/day + unlimited calls. Data auto-renews at midnight so you don't need to top up unless you're a heavy user. Roaming is free within India.
If the airport counter is closed
Airtel + Jio stores exist in every city, but the process is longer without the airport preferential paperwork. Ask your hotel to book a doorstep visit; ~1 hour once the agent arrives.