Get as prepared as you can and check-in online before you fly. Some airlines allow you to check in online 24 hours before so you just drop your bag at the airport, saving you having to wait in the queue to check in. If you do have to check-in a bag at the airport, take what you need with you on your carry-on and pack everything else in your hold luggage.
Book airlines that allow on-line check in and offer a bag drop service. By taking advantage of this you are more likely to get the seat you want in advance. When you arrive to the airport you can either head straight through security with your hand luggage or quickly drop off your bag at the dedicated desk.
Be smartly dressed, polite and well spoken, make good eye contact with the immigration official and have a clear idea of where you are going next (name of hotel, car hire). Never ever make jokes and do not use your mobile phone.