Start behaving like you’re in your target timezone as soon as possible; this includes eating breakfast on the plane at the wrong time. Not always convenient if your flight doesn’t serve meals like this, but they did when I flew to Japan. :)
If you need to stay awake, play at a computer or watch TV because the light emitted from the screens mimic sunlight and could prevent melatonin from being released, which is what makes you tired (and explains why people who play computer games or watch TV at night seem to be able to stay up later).
It’s easier to stay up late than to sleep early, so if you can, plan this kind of jet lag combat technique (i.e. rather than trying to sleep at your new timezone which seems too early, stay up all night and day and try again tomorrow – you’ll be shatttered, and be able to sleep well).