Hi @brent,
There has already been good advice, but two additional things should also help reduce eyes strain: remember to blink (it appears obvious, but staring at monitors for a long time will make you blink much less, which makes your eyes very dry) and avoid using white lights to lit the room you're in (@Harvey already gave the advice of avoiding fluorescent bulbs, but if you do use them, yellow light is better).
This might depend on what you do for a living and might be hard in a computer-related job, but if it's possible do print large amounts of text to read them on paper (e.g. a 20-page paper). It's worse for the environment, but better for your eyes.
And, obviously, if your symptoms persist, go to an eye doctor to see if you need glasses. I went for a year between needing glasses and going to an eye doctor to check my eyes because I kind of got used to seeing worse. I'm not a medical doctor, but If you start to regularly feel that top and bottom lines get blurry when reading (both on digital formats and paper) or if you have greater difficulty reading distant things (e.g. a license plate or a billboard across 10 meters away) you might need glasses. It's better to start using them sooner rather than later. Oh, and this also seems obvious, but eye lenses also make your eyes drier than using eye glasses.
I would avoid any kind of glasses with bad lenses. I never used the kind of "monitor light glasses" that have been mentioned, but I spent my teenage years using glasses with shitty non-prescription yellow and orange lenses (I thought they went great with my baggy pants...) and I still believe that they contributed to my current eyes problems.
I do apply eyes drops some 4 times per day (recommend by my eye doctor) and it helps it your eyes are dry, but it's not a miracle drug.
Using night light (on Budgie) really helps, both with eye strain and with sleep quality.
Good luck.
