It's super easy. It's like a lap belt in the car with a locking latch plate, the only difference is that because of the way the buckle falls, you put both sides through the belt path and then pull tight.
If you have a child old enough to play with the buckle and who might get it undone, you can ask for a seatbelt extender, so that you can adjust it so that both buckles are out of the belt path. Then tuck the ends down so they're less tempting.
Good luck! It's really not hard.
Also, please try to either bring the base on board with you, pack it well-padded in your checked luggage (bubblewrapped is a good plan), or leave it at home entirely (so you'll need to practice a seatbelt install without the base anyway- and might want to bring a locking clip and know how to use it in case a retractor makes it tippy.) A base that is checked (even gate-checked) unprotected can be seriously damaged without you knowing it. So if you plan to use the base, best choice is to bring it on board (it will probably fit under the seat in front of you, it will be one of your carryon items), second best is to pack it safely. Another option would be for whoever will pick you up on the other end, if you're staying with friends or relatives, to get a base to have on that end (either buy and have shipped to them, or they can borrow from someone you trust with your baby's life to have taken care of their base.) Just make sure they have the correct one- there are now SnugRide 32s, 35s, 30s, and 22s, and while the 32, 35, and 30 can all use the same spare base, the 22 can not, and the other 3 can not use the 22 spare base!