First things first. Have you got a valid passport? If not, there’s still time to sort one out.
Next, go to your airline’s website and check their baggage policies. If you are planning to check in a bag, you may need to pay for it separately. Do so before you get to the airport. If you’re not planning to check in a bag, make sure the dimensions and weight of your carry-on bag comply with the airline’s policies. If it doesn’t, you will have to pay to check it in. Also, make absolutely sure you understand the rules about what is prohibited to take into the aircraft cabin, and the restrictions on carrying liquids.
Given that you are unfamiliar with airports, I suggest planning to arrive at least 2 hours before the scheduled departure time. Most airlines allow you to check in online, and to download your boarding pass onto your smartphone. If you have an iPhone, you can keep the pass in the wallet app. Alternatively, most airlines now have self-service check-in machines at airports which are similar to supermarket self-service checkouts.
When you get to the airport, head for Departures and look for signs to ‘bag drop’ if you need to check in a bag. Then, keep following the departures signs to the security checkpoint. This is the stressful bit. First, scan your boarding pass at the barrier. There should be uniformed staff to point you in the right direction. Then join a queue for security scanning. When you get to the scanner, grab a tray then put your carry-on bag into the tray. Take your laptop/tablet out of your bag and put it in the tray. Empty your pockets into the tray. Follow the security staff’s instructions and go through the scanner. If it bleeps, you will be searched by someone of the same sex. Your bag may be searched randomly. Don’t take this personally, the staff are just doing their jobs.
And relax... look up at the screens to find out which gate your flight departs from. When the screens say ‘boarding’, follow the signs and make your way to the gate. Follow the staff’s instructions on when to board. Have your passport and boarding pass ready for inspection. Get on the aircraft.
Enjoy your trip!