I've got weather radios and stuff like that for early warnings, alerts coming to my cell phone, etc. While it's not like a hurricane where you have days worth of notice, they *usually* don't just pop up out of nowhere, they're often accompanied by other severe weather, t-storms, etc. If there are other severe weather indicators, use your head and try to avoid unfamiliar areas or, at a minimum, familiarize yourself with where you are and pay attention to your surroundings so that you have an idea of where to seek shelter if something like that happens.
There are resources available to help train people for what to look for and how to understand what is going on with the weather. The NWS weather spotter training is a good thing to take for interested people.
http://www.nws.noaa.gov/training/wxspot.phpI used to work with a guy who was at his kid's soccer game when a tornado touched down right at the school. It wasn't even a very powerful one but he said it was terrifying and he never wanted to see another one.