I program computers for a living so I often spend 10+ hours a day in front of my computer, so this is something I have thought about a lot, a few tips:
1) Have your eyes checked, glasses can help. I only wear glasses for computer use but without them I have headaches in 20 minutes.
2) Lighting, if the room is too dark or too bright it can hurt your eyes.
3) Adjust the setting on your monitors, though with flat screens the highest resolution will give you the best quality. However you can also adjust contrast and brightness as well as color tone.
Also take a break every 20 minutes or so, even if only to go get a glass of water or the like.
I hope this is helpful.
Zach