All helpful answers, but I have one more that I find more useful.
Buy a phrasebook. Learn some phrases, MAYBE, but carry the book.
Even at airports, it can be fun to use the phrasebook. People can use it to point to things for you. You do not need to be able to say things, or learn things.
Just point to things in the book. I wave hands & point a lot. It can be great fun. I usually do not have trouble in foreign airports. Airports are good: there are many people. Someone will help if you are really stuck.
Chinese are very common travelers, these days. I suspect that all airports have access to Chinese translation, if you really need something.
Mostly you will fine with just a few words, Customs, Immigration, luggage pick-up, baggage pick-up, (remember to note which number, there are sometime MANY places).
Some parts of Korea have a cool service. You get a bilingual buddy. If you get really stuck, you call your buddy & they talk to people for you. You could also try doing this.
BUT, biggest thing to remember in airports: BE CAREFUL. Many people, almost all people will help you & smile & be happy. Some people are not kind, some are quite unkind. Do not carry anything for someone else. Read the warnings about international travel before you go. Millions of people travel: you will be fine if you are careful.
If you don't want complications, check out what you can not take & don't take that stuff.
What stumped me arrive at Beijing the first time? I knew toilet & way out. But I could not tell a taxi from a commercial car. Learn or carry a copy of way out, exit, taxi, toilet, & maybe no entry, staff only. :) But mostly just copy everyone else. :)
Wherever you go there are little forms to fill in. Usually there is someone to help near. learn to ask for a Chinese version?