The other day I forgot my sunscreen and acquired quite the nasty sunburn after only forty-five minutes of working my garden. How did fair-skinned people deal with this before sunscreen was invented? Just get burned over and over until they were tan?
While not only being naturally tanner than normal, they'd also wear thin, loose clothing around their upper bodies and faces, as well as hats of some sort that cover the head and neck (Like the traditional cowboy hat). Generally, though, they'd just burn, especially if they're poor.
They wore hats! In the ancient Mediterranean farmers and shepherds often wore a wide-brimmed hat called a petasos. Middle Eastern people wore (and still wear) the Keffiyeh. American pioneers had their "Stetson" cowboy hats and Mexicans had their Sombreros. And of course there is the stereotypical conical hat of East Asian farmers.
Here's a recent similar question with links in the comments to FAQs of the same nature. The simple answer is usually to keep oneself covered. Even with sheer white linen covering very pale skin I don't get sunburned easily.
It's worth noting that you probably live in a different environment than your ancestors. If your ancestors were from Northern Europe and you live in the USA or Australia, you are receiving much more UV than your ancestors would have gotten.
Take a look at this map:
http://www.lenzing.com/typo3temp/fl_realurl_image/uv-stability-world-map-d2.jpg
If your ancestors were from England and you now live in Washington DC, you've gone from about 90 to about 130 KiloLangleys. That's an increase of more than 40%, and it could easily be worse. A Scot or Swede that moves to Miami or LA doubles their exposure.
Your skin may just not be adapted to your environment.
