Get a weather radio if you don't have one. For about 20-40 bucks, you can get one with rechargeable batteries and a charging cradle. Follow the instructions to set it for your regional station. It will wake up and sound the alert for any warnings in your area. Plus you can actively listen to it for the latest storm news.
As long as you still have power & internet, your local tv station will usually stream during weather emergencies. I've done this on more than one stormy day. Sat comfortably on the couch watching one stream on the iPad while another played on the television. Wondering if this was going to be the day when it finally hit.
On your phone, get RadarScope. It's highly worth the 5 or 10 dollars. It's a detailed radar app. Has many different radar products. Can see the usual storm views with warnings outlined. the relative velocity to see the spin. correlation coefficient to determine if there's a debris ball. Etc. Shows the estimated tracking path for storm cells. For the many storms in my area, this has been invaluable.
Probably the most important resource is NOAA's local prediction pages and the Storm Prediction Center (SPC). During storm seasons, the SPC's Convective Outlook is worth checking at least once a day to see if anything's likely in the near future. Plus the mesoscale discussions are useful on the storm day to see how the forecasters think the events will play out.
For local reporting by locals, Twitter is surprisingly useful. Look for a hashtag that contains the two letter abbreviation for your state plus the letters "wx". I follow #kswx for Kansas storms.