Sunburn is caused by excessive exposure to ultra violet radiation (UVR). Sunburn and the subsequent increase in melanin production, resulting in a tan, are the body's normal reaction to direct damage to the DNA of skin cells.
Because of the thin atmosphere of higher elevations (resulting in less filtration of UVR), and the intense glare of snow and ice, burns can occur more rapidly at high altitude than on a tropical beach.
Symptoms can occur in a few minutes at high altitude and usually start as redness and pain in the affected area. The burn can continue to develop for 24 hours or more after exposure, and in serious cases symptoms may progress to blisters in the affected area, swelling, fever, and nausea.
Minor sunburns can be treated by aloe Vera gel or other relative skin creams. More extreme cases may require some hospital time. I had a pretty serious case one time on my legs, to the point where I felt sick and could barely walk. Of course, like so many other things, the best treatment is prevention, and most UVR damage can be prevented by the proper use of sunscreens and clothing.
At altitude, you should cover as much skin as possible with clothes, and the rest should be covered with sunscreen of at least SPF (sun protection factor) 15. This should be applied 30 minutes before exposure and re-applied 30 minutes after exposure. Usually this will suffice for all day.
Of course, if you are sweating a lot, or constant rubbing of clothing wears if off prematurely, or if you are really fair skinned, you may need to re-apply sunscreen more often. Remember to protect your lips as well with a full-blocking lip balm.
Also remember to apply sunscreen to the underside of your chin and nose, as well as just inside your nostrils and ears, because the intense sun at altitude reflecting off snow and ice can burn these areas as well, even if you are wearing a hat. Some people have actually been sunburned on the roof of their mouth! So try keeping your mouth shut (no insult meant here), and breathe through your nose as much as possible.
The eyes are very sensitive as well and you should always wear sunglasses with 100% UVA and UVB protection. Ideally these should have side shields to prevent reflecting UVR from sneaking in.
Last but not least, follow all of these precautions even on a cloudy day at high altitude, where only the thickest of clouds will prevent any sun damage from happening.
And one more very last thing (more like a PS, I guess): Some people like to use zinc oxide cream as a sun block at high altitudes, especially in the Himalayas and Andes, but this can be rather greasy, messy and hard to clean off your face; however it does supply superior sun protection.