Tip #1: Make a plan and make sure everyone knows the plan.
Planning is key when traveling with kids. Before we head to the airport we remind our kids about all of the steps involved in getting us from Point A to Point B. We narrate the whole day for them and make sure to focus on the fun parts (like the new airplane activities or snacks). We also talk about how we are going to go through security and board the plane, behavior we expect on the plane, and who is going to sit where (so there is no fighting). When everyone knows the plan (even our two year old) our day seems to go better and now that we've flown enough times our airplane travel has a certain rhythm and predictability to it (right down to when to expect meltdowns).
Tip #2: Lower your expectations
I used to be a pretty anxious flyer when my kids were really little. Over time I learned to envision in my head the worst possible scenarios that could happen on our flight (i.e. run out of diapers, majorly delayed flight, sick kids) and then I prepare for the worst. Sometimes our flights are near perfect and sometimes they are nightmarish. But, I never expect things to run smoothly and then, if they occasionally do, I am pleasantly surprised. It might seem like a mind game, but by controlling my anxiety I also have been able to stay calm in hard situations and keep my kids calm too.
Tip #3: Customize activities and snacks to each child
Every kid is different. My five year old will watch Star Wars for an entire flight over and over again and my six year old likes to color and do crafts. My two year old changes what she is interested in every single time we fly. I feel that my role as a responsible parent is to make sure my kids have enough stuff to do (and eat) on a flight so they do not bother other passengers. I know we can only do our best, but at least I always know I've tried to help my kids be respectful of other people. I keep our travel backpacks stocked with dollar store toys and activities and leave them in our travel closet. My husband's job is to add new game and movies to the iPads before each flight. We change up the iPad content depending on our kids' current interests. Everyone's backpack content is slightly different and my kids love having a few new things to do. The anticipation alone about the fun new things in their backpacks usually helps us to motivate good behavior from the airport parking shuttle until they board the plane.