When you arrive at the airport, the check-in staff asks you for your ticket and passport and you have to give them those, and they ask you about where you want to sit, window seat or aisle seat or middle seat. Window seat is the seat right next to the window; aisle seat is the seat in the middle of the plane, beside where passengers can walk, and between those two seats, there is a middle seat. It depends on the size of plane, there might be two seats or three and four seats together.
Now you have your seat, what you have to do next is to take care of your bags. A lot of time, you might have a carry-on bag to take with you. Basically, a carry-on bag needs to be small enough to fit the overhead compartment. If you have larger bags like suitcases, you need to have them checked by the check-in staff and you will pick them later when you land.
When you show up at the airport, you will give the check-in desk your ticket and in turn they will give you a boarding pass. When you get a boarding pass which can have all specific information about where you are sitting, which plane you are getting on and which gate the plane is leaving. The ticket usually does not have a gate on it and some information might change, so if your plane is a little late then your boarding pass should have up-to-date information. There is always a boarding time on the boarding pass, usually a half an hour before the plane leaves. So you always go early in case there is something else comes up.
Now we wrap up by reviewing the steps to check in. Basically, you come to the airport; you have your ticket and passport; then you go to the check-in counter where you are given a boarding pass back which includes all necessary information and they ask you for your baggage as to whether you carry them on or you like to check them in and what kind of seat you prefer.
Hopefully, this information will help you a lot in how to do a check-in at the airport when you are first flying to another country. This guideline is also important to you, whereby you cannot understand all the procedures of embarkation at the airport.