Several years ago we made a trip to Australia and in order to save money on our airfare we ended up making the trip in three increments--a total of twenty-eight hours when you added flight times to layovers. The flight between Australia and California (probably LA) was at least thirteen hours and then there were two more flights to get home. I remember the last layover where we were at about a twenty-four hour mark and needed to stay awake to be sure we'd make our flight home. Without taking a little time to refresh, I don't think we'd have survived it all. Here are some tips for those marathons.
Pack a carry on with a refresher kit. This is a little harder with all the TSA requirements now but not impossible. In your 311 bag, pack a sample size toothpaste and brush, a washcloth you don't mind throwing out (or pack an extra Ziploc to carry it when it's wet), a small bottle of your favorite spirited body wash (something with eucalyptus or a strong clean smell helps) and a small deodorant. Sometimes the airline provides a little kit but usually if you are flying economy, it won't happen. With your refresher kit, you can pop into an airport restroom and wash your face and brush your teeth and feel at least 80% better.
It helps to pack an extra shirt or top to change into as well especially if you've slept on a really long flight.
Some airports have lounges with showers available. You might want to check ahead for that possibility especially if you expect to land and have to immediately go to a business meeting or do some sightseeing before checking into your hotel. Very few hotel rooms are ready when you need them. Airport lounges often offer a day pass so that you can avail yourself of the showers.
Got a long layover? See if there is an airport hotel close by (often they are even attached to the airport). Sometimes they will offer a day rate for you to use a room for a few hours to nap and/or freshen up. If that's not available, they may let you shower in their spa area for a small fee.
If you arrive at your destination and try to check in early at your hotel, you will most likely find the room not ready. Again, there is the possibility that they will let you freshen up in their pool or spa area and most certainly will offer to keep your luggage for you until you can check into your room.
A flying marathon takes as much preparation as any other marathon but with a little planning you can survive and the payoff is usually a wonderful destination.