Make sure to reconfirm your flight 24-hours in advance before going to the airport.
Arrive at the airport with plenty of time to relax after checking in for your flight. Allow 2-hours prior to your departure time and more time certainly would not hurt.
Upon check-in for your flight you will need your passport, any visas required for your final destination in your passport, all necessary documents for minors traveling with you, your flight confirmation, and proof of immunization (if required by the country that you are visiting).
Make sure that you personally check in each piece of luggage with the counter agent and confirm that they are checked through to their final destination or if you have to claim them along the way and recheck them. Do not allow anyone else to check them for you.
Present the necessary documents for your flight(s) and reconfirm the boarding passes with the counter agent making sure that you have received all boarding passes for your flight.
Once you have your luggage receipts and boarding passes returned by immigration, proceed to the security check point and be prepared to present your passport, and boarding pass to be processed through the security checkpoint. You may be singled out for a secondary search that may include being manually searched and your carry-ons completely inspected.
NEVER act in a defensive or aggressive manner during any of the above processes. NEVER joke or give any of the people in charge of the processes a reason to single you out. Many vacations have been ruined by folks taking offense to the processes and thereby being delayed and missing their flights.
Arriving At Your Destination:
Once you arrive at your destination you will be deplaned and ushered into Immigration. You will need to present your passport and allowed to enter the country.
You will then proceed to luggage claim where you can then claim your luggage. Make sure that your luggage has not been tampered with and if you have placed anything of value in your luggage, be sure that it is still there.
You will then be required to go through customs to exit the baggage claim area. You will be provided with a customs declaration form on your flight. You will be required to submit this form to the customs official to clear customs
NEVER try to take undeclared items through customs. If you are singled out for a secondary search and they are found you may be deported right then and there, or worse.
Staying Safe: Once you enter the main terminal at your destination, do not respond to people asking if you need a taxi, transfer, tour guide or any other service. If you are being met for a transfer to your hotel you will see them waiting for you with your name on a sign. If you are going to negotiate for a transfer to your hotel, most airports will have a taxi stand or queue that you should use. NEVER respond to someone offering you a service after approaching you.