Inexperience with jet lag put a damper on my first overseas trip. I was 18, and my mother took me to London as a graduation present. I felt groggy and unable to make decisions, and was generally crabby for the first half of the trip. Since then I've made several dozens of trips across many combinations of time zones, and have learned a few things that really help me to feel as good as possible despite jet lag.
Try to move yourself, even a little bit, toward your destination time zone.
In the week before your departure, try pushing your bedtime and meal tines forward or backwards as needed. I have had good luck with shifting by half-hour increments each night, and can generally push myself about three hours toward my destination without wrecking my daily life at home.
Advanced Tip: Take melatonin and tryptophan about an hour before going to sleep. If you are a caffeine drinker, do it at times compatible with your destination.
Get and stay hydrated.
Unless you already have a good hydration habit, work on it in the week before your departure. It's such a simple thing, but having enough water in your system really does seem to head off a host of travel discomforts.
Advanced Tip: Counteract the diuretic effects of caffeine and alcohol with extra water.
Sleep on the plane as appropriate for your destination time zone.
For an overnight flight, try to sleep as much as possible, using a sleep aid for flights longer than eight hours. For a day flight, take a short nap or two but try to stay awake so you can really sleep the first night at your destination.
Advanced Tip: If you really want to sleep on the plane, bring an eye mask and stick a note on it that says "Do not wake me for meal service."
Get active on arrival.
Do not just head to your hotel and collapse. Chances are your room won't be ready for hours anyway. Do something that keeps you moving but isn't mentally taxing. A leisurely breakfast followed by a walk in a park and window shopping usually works for me. Once I check into my hotel, I take a shower and decide what to do next. Another sight-seeing walk is a great idea, but sometimes I just lounge around and watch TV until about 8pm, when I'll let myself go to sleep. Listen to your body: if you feel up to a museum or a boat ride, do it, but if you're feeling quiet and overwhelmed then don't push yourself.
Advanced Tip: Apply caffeine only before noon at your destination.
Get up at a reasonable hour in your new time zone.
If you're heading west-to-east, you'll be tempted to sleep late. Don't, even if it requires setting a "just-in-case" alarm for 10am. If you're going the other way, you'll be waking up really early. If you can convince yourself to cat nap until six or seven AM that will help a lot.
Advanced Tip: If you absolutely can't sleep when it's night time at your destination, let yourself be awake. No sense stressing about it. A few years ago I went to Cambodia with a friend. We both ended up waking in the middle of the night due to jet lag. We made the best of it by having a tea party our first few nights: we'd wake up, have cookies and something to drink, and would read and chat until we fell asleep again. Our tea parties generally went from about 4-6am, and we'd get up for real around 8 or 9.
Eat during the local meal times.
If you aren't hungry for a real meal, then have a snack.
Advanced Tip: Make breakfast or lunch your biggest meal of the day.
Be kind to yourself.
You might have a big agenda of sight-seeing and shopping planned, but if you start feeling crappy then you start feeling crappy. Do enough to make you feel satisfied without pushing yourself to the point where you aren't really taking things in or enjoying your experience.
Advanced Tip: If you need a nap in the middle of the day, take one. Make sure you set your alarm for 20-30 minutes so it doesn't turn into full-fledged sleep and really knock you off schedule.