Getting rest while you're traveling is incredibly important — enough shut-eye not only keeps your immune system strong, so you can avoid catching the local bug, but a good rest ensures that you will be able to really enjoy the new place you're exploring.
When I'm traveling, I notice people making so many mistakes when it comes to avoiding the worst of jet lag. I have flown between New York and Sydney more than a dozen times in my life, and if that's not a trip to test my theories, I don't know what would be. (I've also done probably about 10 trips to Europe and the U.K., and spent time in Northern Africa several times, and these techniques have been tested on all those trips). Here's what works for me.
Cut back on sleep the night before a flight: I normally sleep eight or nine hours a night (so you can tell I'm serious about this subject!), but I never rest more than four or five the night before I fly anywhere, no matter how long the plane trip. Usually I'm up packing and too excited anyway, but this cutting back the night before means that even if I nap on the plane (it's inevitable), I'm still pretty tired by the time I arrive at my destination, which is what you want to aim for, even if you arrive at noon.
No caffeine before flying or on the plane: Your anti-jetlag plan should begin before you even leave, and this means that even before you take off, no stimulants, which are only going to confuse your body clock. Alcohol and caffeine are verboten while flying for anyone who cares about their health anyway. When you land, if it's early and you are tired, some green tea can get you through Day 1, but I wouldn't recommend anything stronger than that if you want to get some rest when you need it.
Snacks, not meals: I always need to have something in my stomach when flying, otherwise I can get a bit nauseous. So I snack before and during flights, always keeping a little something down, but never eating a meal. This keeps me satiated, but also knocks off my eating rhythms, so that I'm not 'expecting' a meal at a certain time which might not be appropriate when I arrive at my destination.
Your destination time is the only time: As soon as you get on the plane, start thinking in your destination time. I see many people spending their entire vacation four time zones away thinking about what time it is back home. Set your watch when you land and don't look back. You are now on a new time, and that means staying up until it's a reasonable time to go to bed, eating on your new schedule, and no napping! Force yourself to stay awake until everyone else retires, you should be tired either way if you didn't get enough rest the night before. Make sure that on your first night you get at least nine hours of sleep, and wake up on your new schedule.
Get (real) light: If you are on a plane that's arriving in the morning at your destination (like a red-eye flight to Europe), open those window shades an hour before you arrive, and bathe in the morning light. Yes you will annoy some people on the plane, but those people won't be enduring your jet lag and they will have to suffer from their own bad habits. Besides, that's what those eye covers are for. When you arrive at your destination, be sure to get as much natural light as possible. And when it's time to go to bed, be sure to sleep in an entirely dark room. All of these suggestions will result in sounder, better sleep.
Melatonin: Some people report that melatonin supplements really assist with jetlag. I've never taken the stuff, but it might be worth a try.
These ideas should all help you adjust to your new schedule and keep getting rest.