Check-in at the airport is free and usually starts 3 hours before departure, while Bangkok Airport counters are open all day. It is recommended to be at the airport at least 90 minutes before departure.
It is also possible to check in online using the website or mobile app 24 hours before departure and bring your ticket printed or just in the form of a barcode on your mobile phone. You can then check in your luggage at the "Baggage drop-off" express counter.