I work in IT so I have to look at screens a lot. Blue light which screens emit a lot of will increase eye strain / headaches and from memory reduces your natural blinking rate leading to dry eyes.
For those that worry about eye damage related to screen usage. I have spoken to several optometrists and GP's and they have all agreed long term screen usage does not cause eye damage, only strain. The reason I asked them is because I had been told by countless people all my life "You'll need glasses by the time you're 25". Well... I am 37 and I have 20/15 vision. Which is better than 20/20 vision, so suck it!
Avoiding eye strain
The most obvious is taking a break. Look away from the monitor and focus on something else for a bit. Go for a walk, make a cuppa, whatever it is you can do to give your eyes a rest.
The yellow Gunnar glasses do help in this regard. But I don't like wearing glasses all day or seeing everything with a yellow tint, also the frames pushing on the temples can cause headaches themselves depending on how well they fit.
How early in the morning you start has a significant impact. If I get up and go straight to work (short commute or working from home), just 1h~ of usage frequently results in a headache / blurry vision / dry eyes and it lasts all day. I have found for the first 2h~ of being awake that if I make sure to look away from the screen more often and find other jobs that don't require a screen or reading then I have no issues.
Turning down screen brightness is not a universal solution, how bright your monitor needs to be is dictated by how bright your room is. The darker the room the less bright the screen needs to be. A brighter room requires a brighter monitor for you to focus properly and counter glare. You need to find what works best for your setup. Also note that adjusting brightness will have an affect on colour accuracy and require you to recalibrate for colour sensitive work.
Fluorescent bulbs are not ideal and can be really bad depending on their colour temperature and your sensitivity to it. Not much you can do about that at work but if they flicker, demand they are replaced. Get some natural light in but watch for glare.
Night colour / redshift / applications that switch your monitor to use more red light during evening hours can be kinder to your eyes.
Usage of dark themes both for your system and websites is also a good idea. If a website does not have a dark theme you can use a browser extension such as Stylus available for Firefox and chromium based browsers which can be used to find and apply community created themes to most websites. The themes are not great, some have minor issues that make some parts of the site harder to read but if you know CSS you can adjust/fix them or write your own.
