There are several things to consider.
1. Reduce the brightness of your monitor. Especially if you are staring at white screens a lot, such as much of the internet. Whites can be quite bright. I have my brightness way down.
2. Indirect light. A bright light coming into the sides of your eyes, such as sunlight through a window can cause strain and may not be something you really notice. Blocking off that light can make a big difference.
3. Contrast. This I imagine varies a bit by person, but you can play around with the ambient light relative to the computer screen. My work area is darkish, but not too dark. For some people a lighter work area might work better.
4. Monitor. Some monitors aren't very good. Most people don't really have the old crappy ones around anymore, but it might be worth getting a newer model.
5. Glasses. They actually make glasses that are optimized for computer use. Don't know much about them.
6. Take breaks. It's good to stand up frequently anyway. It is also good to give your eyes a break, so stand up once and awhile and do jumping jacks or something.