Right, you have to tell your toddler it's an adventure, but with chocolate! When you get to airport, get a trolley. Have change ready and know how much it will cost. Try and carry as little as possible. Think I had one carry on bag. DS (23 months) had a Little Life back pack, so he carried his own crap stuff. DD also had a backpack with her coloring books.
Had a buggy that collapsed and was able to take it to the plane. Hopefully you won't have to walk up steps to the plane like we did. Anyway, ask the cabin crew if they can keep it on board, otherwise you will have to pick it up in baggage claim.
Going to the toilet was tricky, but there was a very nice flight attendant who came to watch either DS or DD if I needed to go or take either of them. Eating was interesting, but try and keep it simple. Don't try and get too ambitious and just eat the roll unless you want the chicken with tomato sauce (because it's always something with tomato sauce) on your lap. Same goes for hot drinks. If the flight attendant offers you something, automatically think, 'this will end up on my lap...' 
Some people swear by night flights, but I've found it more difficult as kids get over tired.
You will find people are incredibly kind. After a flight from London to New York, we were on another flight from New York to Los Angeles. There were 3 seats, and DS was technically on my lap, and another man who very unfortunately was sat next to us, offered to move so we could have more space 
Security: Take your time. Get your toddler to run through the x ray machine (but not down the concourse, as DS did in New York causing 5 security guards to chase him
). try and get your toddler to put on/off shoes on their own. Ask if you can take the baby through in a buggy. They have a hand held security device they can use. I was lucky once in Heathrow and they used it as DS was asleep and they didn't make me wake him up.
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Only other advice would be to pack a fleece and/or layers as the plane can be cold. Pack as light as possible.
It will be fine. Kids do adapt and as one flight attendant said to me once, 'in my 20 years of flying, have never known a baby to cry the entire flight...' 