There are three ways to check in with British Airways, all free of charge.
Classic airport over-the-counter usually starts 3 hours before departure and ends 45 minutes before departure.
Online check-in starts 24 hours before departure, when you can also select seats on the plane for free. The most convenient way without having to print a boarding pass will be mobile check-in, also 24 hours before departure. However, you need to download an app, then just show the barcode on your mobile device at the airport and you don't have to wait to print your boarding pass.