1. Check-in online as soon as possible. Most airlines let you check-in for a flight 24 hours in advance. If you don't have a pre-assigned seat and you want a chance at getting the best seat possible for your fare class (there are different fare classes beyond just coach or first), check-in early. Be aware that some airlines charge a fee if you don't check-in online.
2. Get there early! This is obvious, but it cannot be stressed enough. Other than the holidays, summer is the busiest leisure travel time which means there are lots of people in the security lines who are unfamiliar with the process. Unless you have TSA Pre-Check or elite status on an airline, be prepared for long security lines. My friend Jess reported that the security line at Bradley International (Hartford, Connecticut) took more than an hour last weekend.
3. Plan for delays and cancellations. Even if it is bright and sunny at your home and at your destination, there can be delays to your flights. Before you get to the airport look at alternate flights to your destination that are available on your airline. You can do this by doing a dummy booking on the airline's website (stop before the field asking for your credit card). Write down those flight numbers and keep them handy in case of significant delay or cancellation. This will save the airline agent time and relieve a bit of your stress if you know what your options are.
Remember this when delays and cancellations occur; the airlines don't like delays any more than you do. The gate agents, flight attendants, and phone agents are probably more stressed out by the delay than you are. Getting huffy with them and saying things like "I'll never fly this airline again" won't help you or anyone else. (Insider info: Most flight attendants don't get paid for time on the ground when the aircraft door is open).
4. Know your airline's reservations desk phone number. When your flight gets delayed or cancelled you will have to wait in line to see an airline agent. Get on the phone with the airline's reservation desk while you're waiting in line. Often you will get through on the phone before you get to the front of an airport line. Give the phone agent the alternate flight numbers that you found before you left your house.
5. Bring a small power strip and make friends. There are never enough outlets to go around in an airport terminal. Bring a small power strip (I found one at Walmart that has four outlets with a one foot cord) and then you only need to find one outlet to charge your phone and those of your friends, family, or strangers.
6. Join the airline's frequent flyer program. Even if you only fly once a year, join the frequent flyer program. You can use the miles for things other than flights. For example, I only fly on United and Delta when US/ American doesn't fly to where I'm going. I collect miles from those trips and have used them for magazine subscriptions, gift cards, and even "bought" a coffee maker through frequent flyer miles.
7. Pack snacks. If you're traveling with small children, you probably have this covered. For the rest of us, it's a good reminder. I always pack a Clif Bar or two in my laptop bag. It's amazing what a couple of hundred calories can do for your mood during a flight delay.
Bonus tip for the nervous flyers: I was once a very nervous flyer too. That changed once I realized that the pilots want to land safely just as much as I do. Pilots won't fly unless they feel safe. Those sounds you hear the plane making, they're normal.