Another top tip: buy a bum bag. Carry new nappies and wipes in it, and wear it wrong way round - over your belt buckle rather than over the base of your spine. Much easier to get to the stuff you need.
It's not that tricky. First nappy I did on a plane was my daughter's at 6 months. She pulled the classic trick of peeing between nappy off and nappy on. It became a complete change of clothes, and a nappy change. After that, everything on a plane with kids has seemed easy...