Start with a registration
It is painted on the rear fuselage or under the wing, and usually starts with a country prefix: G for the United Kingdom, D for Germany, N for the United States.
You will get the serial number, when it was delivered, who operates it and whether it is still in service.
Looking up more than one?
Spotter keeps what you find
The same lookup on your own PC, plus a logbook that files the type, airline, date, place and your photos with every sighting. One payment of £4.99, no subscription.