Let me start by saying that most of my experience here is with using my own small manual wheelchair. My needs are going to be different that you’re especially if you’re using a larger power wheelchair.
1. The biggest tip of them is to make sure you communicate well with the airline you’ve chosen to fly with. You’ll save a lot of trouble if you don’t assume the airline knows what you want and what your needs are. This means checking off that you use a mobility device if you’re booking online or letting the booking agent know over the phone.
2. If possible when you’re checking in tell the agent you’re going to keep your chair with you right up until the gate. Also make sure they provide you with a door tag to attach to your chair. This tag lets the ground crew know that your chair should be the last thing to go into cargo and the first thing to come out. Also that it needs to go up to the door of the plane and not the baggage hall with the rest of the stuff (I've had this happen).
Once you get to the gate if you’re unable to walk you’ll transfer to an aisle chair. This is a tiny skinny chair that will fit down the aisle so you can get to your seat.
My understanding is if you're traveling with a power chair there are issues depending on what kind of battery your chair uses. Make sure you check ahead with the airline as you may need to arrive extra early so them to accommodate you.
3. Depending on if you're wheelchair folds or not you may want to consider placing a sign on it indicating this. I've seen airlines try to force a chair to fold when it doesn't. Or try to fold something the wrong way and break it as well. Yes the airline might be liable for damages but that doesn't help when you arrive in your destination with a broken wheelchair.
4. Washrooms on airplanes are notoriously tiny. Make sure to ask in advance if the plane will have an aisle chair on board so the flight crew can assist you to the washroom as needed. Some planes have two washrooms where one is large enough to fit the aisle chair right inside. Some Others have a curtain that go across so the door to the washroom stays open. To me that kind is annoying but I can see it being helpful if you needs to have someone there to assist you as well.
5. Always try and bring some spare parts with you if you're able to. For me this means extra tubes for tires. Also possibly some kind of pump if you're able to fit it in your luggage. For powerchair users an extra charger or at least cable for your charger is advisable. Also make sure the charger can handle the voltage of the place you're traveling too. Or if not that you have a step down/up transformer.
Hope this helps out. Let me know if you have any extra suggestions.