Who needs one
Everyone except nationals of Nepal + Bhutan. India has three visa categories relevant to tourists: e-Tourist Visa (30-day, 1-year, or 5-year), e-Business, e-Medical. Most tourists want the 30-day or 1-year e-Tourist.
How to apply
Go to indianvisaonline.gov.in — that's the official site (many others charge you extra for the same form). You need a passport valid 6+ months from arrival, a passport photo (2×2", white background), and one page of the passport photo scanned. £30 for 30-day, £60 for 1-year, £120 for 5-year. Turnaround: 4-5 business days typically.
On arrival
Print the e-Visa confirmation (yes, printed). Get in the e-Visa queue, not the visa-on-arrival queue. Bring your passport photo (again). Fingerprints scanned. 15 minutes at Delhi + Mumbai in an off-peak hour; 45+ in peak.
Watch outs
Don't over-stay — the fine escalates. Don't fly out from a small airport unless the visa authorises it (some 30-day e-Visas restrict entry/exit to major airports only). Business visa if you're paid in India while travelling.