Am I the only person whose heard of the 20-20-20 rule?
I don't do it, but it is pretty well advised for preventing (or minimizing) eye strain.
http://www.mayoclinic.com/health/eyestrain/DS01084/DSECTION=prevention
Eye doctor here (really). Every situation is different, but the above is a good rule, but more is better. As often as you can remind yourself, take even just a few seconds and look away at something distant. Out a window is best, but even down a hallway works. Near work (reading, computers, knitting, etc.) all involves tightening the ciliary muscle inside each eye to squish the lens in there and bring the focal point to whatever you are looking at. It's like any other muscle, and it will fatigue over time. Imagine holding a 5 pound rock at arm's length. 5 pounds isn't that heavy, but hold it there for 2 hours and your arm will hurt.
In addition, most of us have two eyes. Those 2 cameras for most people align at rest in a parallel position. Near work requires us to converge, or pull the two cameras in to a non-parallel position to maintain a single image. The muscles surround the eye are actually much stronger than they need to be, but the coordination center in the brainstem fatigues over time, similar to a muscle.
The surface of the eye is coated with a thin layer of tears at all times that keeps the cornea from dehydrating. When that evaporates off, the dry surface irritates the corneal nerve endings (that's the burning sensation during a staring contest) and vision blurs because the surface becomes irregular. Studies have found that computer users (laptop, desktop, smartphones too) blink less frequently, and blinking is what redistributes tears on the eye.
Little, short breaks while looking away lets the muscles inside the relax, lets the neurons in the brainstem recharge, and reminds you to blink and rehydrate the eyes.
If that doesn't help, over-the-counter artificial tears are fine to use every couple of hours, but NEVER use a redness relieving drop with a vasoconstrictor like tetrahydrozoline. They can get addictive.
Even folks with "perfect" eyesight can benefit from low powered computer glasses to let the muscles relax a bit, especially if you notice things are blurry after computer work out in the distance (the ciliary muscle is spasming and can't relax). 20/20 in the distance doesn't mean much if you spend most of your life staring at a screen. And a little help during screen time can make it less likely you will need glasses in the distance later on.
With convergence, generally the further the target you are looking at, the less the eyes will strain. Laptops and phones make that tough, but the further the better.
With regards to illumination, there's no perfect formula since every person has a preferred brightness level. But generally you don't want a large difference between screen and background. It takes some experimentation to find your own happy place. If you work in a bright office with fluorescent lighting, a baseball cap is a good, cheap way to block glare from above.