There's a lot of good general advice, but I have a few very specific tips because I've spent far too much time on planes. In no particular oder:
Plan to lose your luggage. I'm a bigger girl, so I carry enough of an assortment of clothing to get by for the trip. Think separates.
I wear leggings or sweatpants, a knit shirt, socks, and a hoodie on the plane. Layers are good and the hoodie can become either a makeshift pillow-like or blanket-like item.
Before landing I wipe myself down with Neutragena face cleaning clothes, change into real pants and fresh undies, and (being girly) put on a little mascara and lip gloss. Makes me feel more awake / put together. Some international airports have showers you can pay to use so if you have a long lay over before your final leg it's a nice use of time.
Brand new socks are a nice treat that make a big difference - even the free ones in business class are cheapo. I usually take two pairs of new ones just for the plane. I like cotton athletic socks with the extra squishy bottoms.
It's already on the list that was posted, but I'll stress that you want an eyemask - the best ones bump out around your eyes and don't put any pressure on your eyelids. Walgreens sells a good one for not much $, stocked right near the earplugs/contact lens stuff.
Earbuds are better for sleeping on planes than earphones. You can lean the side of your head against the back of the chair comfortably. The ones with a squishy tip create a noise isolating seal. And even if you don't feel like listening to music, they are good to have. Putting on headphones is the international sign for "I'm done talking with you, leave me alone."
The U shaped pillows are great, but the blow up ones aren't nearly as good. (But if you must use a blow up one in order to save space the Eagle Creek one is pretty good - their travel cubes are also wonderful to help keep gear organized)
Hydrate - drink lots of water, put moisturizer on your face. I like the crystal light to go packets because I don't like plain ole water so much. White grape and lemonade are the best flavors! I usally take my Sigg bottle because the UA flight attendants usually can't just give you a bottle (because everyone will want one). However, if you take a bottle you want filled up to the galley and explain you just drink a lot of water and don't want to bother them constantly, most will help out.
Try to sleep. I usally just have my dinner before getting on the plane and start trying to sleep immediately. Some people swear by taking Ambien once they are on the plane and some use Benadryl / or a drink. I don't like any of those options and find that it's best if I just come a little tired.
And after the plane gets there - STAY AWAKE!. It's sometimes really tempting but naps are the enemy. Staying in natural light helps. Everytime I've napped I've created massive jetlag for myself. If I stay up past 7 I'm usually ok. I also leave the drapes in the hotel room open the first few days - helps me adjust to have morning light help me wake up.
Anyway, hope some of that is helpful!
Alice