Airports around the world work in the same basic fashion:
Check in -> (Immigration if international) -> Security -> Gate -> Airplane
Some airports have a second security check upon entering the building itself. There are airports with multiple terminals, generally one airline is only in one terminal but not always. Also, international flights may operate out of a separate terminal.
To find your check in location look first for your airline, then for a sign with your flight number or destination and class of service. It’s not unusual to not have separate counters for different flights. At this point you hand over any luggage you are checking, you receive a piece of paper that is your boarding pass. This paper has one important piece of new information–your gate number.
You then proceed through security–your bags will be x-rayed, in most airports you will walk through a metal detector, but other technologies are also in use. In general any garment which covers normal street wear must be removed and sent through the x-ray. Look at what the other passengers are doing, some airports require shoes and belts to go through the x-ray also.
You then go to the gate listed on your boarding pass. When you get there doublecheck that it’s correct (see what flight is shown on the signs at the gate), changes occasionally happen. There will be screens around listing flight numbers, cities, gates and time.
Once you’re on the plane pay attention to the safety announcement even though you will see most people are ignoring it–other than the location of the exit doors it’s basically the same for every flight, experienced travelers already know what they’re going to say.