I'm in Japan every month so, 10-12 hour flights are pretty much the norm these days, so some quick suggestions.
If first/business is not an option, choose an isle seat, check seat maps and try to find isle seats without a nearby passenger if possible, extra space always helps. 1/2 the distance to the restrooms is usually a good place to be, not too close not too far since you don't want to be dealing with people going by you all the time but want to remain accessible.
If possible choose a modern aircraft to travel on if you have not chosen your flights already. Most modern airplanes like the B777, B787 have good IFE systems that will keep you entertained without the need for an iPad/Kindle/etc.
Stay hydrated but don't overdo it, try to avoid alcoholic beverages if possible since alcohol is a diuretic. Bring your own light snacks, since most airplane food is not really that great. (does not usually apply if you are flying First or Business, but even they can be abysmal at times)
Wear comfortable clothing, and comfortable shoes, long socks. A light jacket to keep your body temp constant during the flight.
Find a good set of headphones/earbuds/etc. They don't need to be noise cancelling if you are not used to them (some people get headaches due to the constant out of phase sound that is generated by the headphones), but want them to be pretty good at inhibiting the white/background noise from the engines.
Depending on the direction that you are flying, it might make sense to sleep or not to sleep on the flight in order to avoid jet lag. In my particular case, I only take a short nap going to Japan since I arrive in the late afternoon, and I'm back in sync with JST the next morning after getting some sleep. From Japan I try to get 4-5 hours of sleep in order to mange jet lag better when I am back in the US since I usually arrive around noon and force myself to stay awake till at least 10 or 11PM.
Make sure to take vitamins/supplements with you, so that your body's immune system is in tip top shape during/after the flight to Asia and your flight back.
Workouts are a great way to get over jet lag and to get your body in sync.