With a red eye flight, you're better off if you can sleep on the plane. Avoid alcohol and caffeine but drink plenty of water. When you get to your destination the following morning, stay awake and spend as much time outside as you can to get your body's internal clock set to the sun.
Try to go to bed as close to a normal time as you can.
That's optimal conditions. Here's my personal experience:
I traveled to Europe for the first time last year. I had a night flight out of Philly for the transatlantic leg. I was headed to
Disneyland Paris followed by the 10 night med cruise on
DCL. I was too excited to sleep on the plane. My friend and I arrived at our Disneyland Paris hotel and were told not to even think about checking in until 3 or 4pm. So, in a zombielike state, we went into the park and kept going until around 5pm and returned to the hotel to crash in our room.
I woke up to bright sunshine and seeing the clock said 9am I hopped out of bed and jumped in the shower, ready to take on another day at the parks. After getting dressed, I looked out the window to check weather and saw that... THE SUN WAS SETTING????? Apparently my restful night of sleep was only about 3 hours long. And now I had to wait until I tired out again so I could go back to sleep and wake up the next morning.
Oops.
It took another day before I finally felt accustomed to the time change.