The best way to be prepared is to know what is going on around you. Pay attention to weather forecasts, and when the weather seems questionable, don't be afraid to check on current conditions from your favorite weather information source. I personally like to reference the Storm Prediction Center Convective Outlooks to see an analysis of potential severe weather over the next couple days.
Investing in a weather radio can also be a great investment. Alternatively, knowing which Weather Forecast Office (WFO) serves your area will give you direct access to alert information for your area.
The internet can be a great source of real-time weather information. Consider making a bookmark to your favorite weather information source on your mobile device so you can call up the information on a moment's notice. Some local television stations may also offer SMS weather alerts and/or daily forecasts direct to your phone.
If you enjoy digging deeper into the weather, you could use radar software on your own machines. I prefer GRLevel3 (21 day trial; Windows), but there are other options out there like StormLab (15 day trial; Windows) and WeatherScope (Free; Windows, MacOS).
Most importantly, if things outdoors look dangerous, get indoors and wait for it to pass. Its better to be late to your next appointment than it is to be injured on your way to it.
Internet sources for weather information:
Weather.Gov
Weather Underground
Weather.Com