The process is quite straight-forward (and I did the old version with more steps/paperwork). The hardest part I found was that my mom (who was dropping my pets off at the airport for me as I was already here) misunderstood the timeframe for the tick/tapeworm (she thought it was within 24 hours, rather than 24-48 hours), so there was a bit of a scramble to get to the vet.
You'll need an IATA carrier, and I think it needs ventilation on all sides, and needs to secure with actual screws (not plastic clips or anything). I got mine off Amazon, but then at check-in they decided mine was about 1" too small for my cat so my mom headed to PetCo (or PetSmart) to pick up a larger size (which is part of the reason they want you to check in so early, so that you have time to do that if necessary). You'll also need to attach food/water dishes to the door of the crate.
My cat hates being in his carrier, but he made the trip just fine (albeit at age 5 rather than 10). He was unusually silent on the way home (he's quite vocal/whiny), and it took him about a week once he got here to really settle in and act like his normal self, but he handled the trip just fine, overall. My mom put towels/old blankets in the crates with my dog/cat, both for padding and so they'd have something familiar smelling on the trip. I don't know if it made a huge difference, but they didn't hurt. She also froze water in their water dishes so that it would defrost gradually on the flight (though the blanket in my cat's crate was wet so his may have spilled a bit).