It varies from year to year, of course, but spring and summer are usually the active months. For any one given city or neighborhood, it's pretty uncommon to get the really bad hail or tornadoes touching down. Also, we usually don't get the big giant nasty tornadoes like you see in Oklahoma.
Granted, I grew up here so I'm used to it, but I really don't think it's bad. Tornadoes are scary, but they are super localized. It's not like a hurricane that hits a whole state, you have to be more or less directly in the path to really worry. As for hail, we do get that in our storms, but it's not scary hail. Usually it's peas or maybe dimes. The huge stuff is very uncommon, and even then, it's mostly property damage you have to worry about, not injury to yourself. (Unless you're standing around outside. Don't do that.)
When there's a storm system brewing, the local news meteorologists are totally on top of things. They will interrupt TV to broadcast warnings, and the National Weather Service will interrupt radio broadcasts. There are Twitter streams you can follow, too, or sign up for email/text alerts on websites like Wunderground. Really, though, even without all of that I'm rarely surprised by this kind of weather. During storm season you learn to just kind of keep an eye on the weather, and to recognize the fronts sweeping in. Just check the weather once a day and if there's a possibility of storms predicted, check it again closer to the predicted time. These kinds of storms are usually predictable pretty far out.
Also, make sure to look up storm tips. Your local city probably has information about storms and weather preparedness, as well as anything that might be more specific to McKinney versus the rest of the DFW area. In general, if there's a storm and it's producing tornadoes near you, you want to be in an inner room with no windows and no outer walls, on the ground floor if you have two stories. In most houses this ends up being a bathroom, so you always hear stories about people hanging out in a bathroom reading books and waiting things out. I myself have memories of being sent into the bathroom while my parents went outside to see if they could see anything, lol.