Get hydrated before your trip.
Unless you've already got the personal hydration habit, focus on drinking at least six 8-ounce glasses of water per day leading up to your flight. Yes, at first you'll have to pee a lot, but you also will adjust somewhat. Good hydration greatly reduces the headaches and fogginess associated with long-haul jet travel. Make sure you also drink water during the flight,
Advanced Tip: Add one glass per each alcoholic or caffeinated drink you consume during that day, to mitigate those substances's diuretic effects.
Choose your seat wisely.
If you sleep like a log, get a window seat. If you're a super hydrator, or just like to get up and stretch a lot, go for the aisle. Sitting by the bulkhead or in an exit row can reduce that closed-in feeling, although it does eliminate your under-seat storage area.
Advanced Tip: Check seatguru.com in advance for potential unexpected circumstances at your particular seat such as no window, limited recline, or reduced seat width.
Get to the flight in a relaxed manner.
The less stress you have before getting on the plane, the easier it will be to relax and have a comfortable trip. Leave for the airport early, be organized and prepared for the security procedures, and cultivate a peaceful attitude toward whatever happens between leaving your house and take-off.
Advanced Tip: Eat a tasty yet light meal or snack, if possible at the airport, before getting on the plane.
Dress for comfort in a variety of temperatures.
Wear soft layers that do not chafe or bind. Bring a wrap to throw over your chest, shoulders, or even face when you sleep, as it is often difficult to get an extra blanket (and blankets are being eliminated on many domestic US flights).
Advanced Tip: Airplane bathrooms are small and can get yukky, so avoid wearing anything complex to adjust or that could drag on the floor.
Prepare for sleep.
Bring an eye mask that you are already used to sleeping in, and ear plugs. If those horseshoe-shaped pillows help you, bring an inflatable one. Make sure if you take your shoes off during flight that you have socks to keep your feet warm and clean.
Advanced Tip: For a flight of longer than eight hours, try a time-released Ambien after the bustle of the first meal service is over.
Stretch your body.
If you're awake, stand up for a minute or two every hour or two. Walk to the bathroom, shake your legs, move your arms, anything to break up the pattern you've been sitting in.
Advanced Tip: The galley area gets really quiet outside of meal service times. Try a couple of deep knee bends and toe touches neat there -- just don't hang around long enough to get in the flight attendants' way.