On long flights: make sure to moisturize. The dry, air conditioned air in the plane will make your skin dry. So slather on that nice greasy cream (get some samples at a store before your flight).
Jet lag, my worst was when flying from Sydney, Australia to San Francisco, U.S.A. via Taipei, Taiwan. The flying took me 24 hours in total, but I was only 5 hours further in the day (left at 1pm Tuesday afternoon, arrived at 6pm Tuesday afternoon). I guess there’s not much you can do about such a jet lag, just get through it.
When you get seated in the plane, set your watch to the new time already, and try to live accordingly to it. Have a nap when it’s bedtime, and eat when you should be eating something (breakfast / lunch / dinner).
Flying eastwards: most likely to skip a night, so make sure you sleep on the plane. Try not to have a long nap when you arrive early in the morning. You can nap for about 2 hours, but make sure you set an alarm, and go get some fresh air after that. Especially some exercise will do you good: go for a walk and explore the new area, or when you’re arriving back home, have a little run or workout.
Flying westwards: You’ll have a very long day, so when you arrive around dinner time, go and have dinner, and go to bed around 9.30pm / 10pm.