They sound tornado warnings because they spin up quickly. It results in a lot of false alarms, but without them there would be no warning at all. So, when they sound, be aware--do not fail to be aware, this is indeed serious business--but take Douglas Adams' advice and DON'T PANIC.
With experience, you can learn what to watch for. Tornadoes almost always come from the south/west/southwest. No guarantees. If you see one east of you, you can almost certainly afford to stop and marvel, but watch over your shoulder as well, because they travel in groups, and as one fades another is liable to be spinning up nearby. And don't assume the worse the storm the better the odds. Tornadoes come out of hook-shaped formations at the trailing edge of storms and generally at the south end of supercells. So, there's very likely to be a lull before they come, and often the tornado strikes where the rain has been weakest. And, yes, straight line winds can be as destructive, so just because you don't see rotation doesn't mean you need to be wandering around a junkyard full of loose steel.
There's pretty much always a pressure drop--noticeable--and a loud noise ahead of a tornado strike. But no guarantees. So, if you have no experience with such storms, you are better off safe than sorry.
What is safe? A small room. I once heard a bunch of yankees discussing how slick it would be to spend storms in your car in the garage, because then you have two roofs over your head. Wrong, wrong, wrong. The garage is the biggest room in the house, and if and when fat ceiling beams snap they will fall into the garage. The roof of your car will not stop 4x4s from giving you the headache of your life. Avoid windows if you can, but mainly find a small room which is not on an outside wall with west or south facing. North or east facing outside walls are far safer. The bathtub may or may not provide extra protection if it's cast iron. But the main thing is, if the room is less than eight feet wide you're unlikely to wind up wearing ceiling support beams and rafters.
If you're in a car and you encounter one, if and only if you see it coming from a mile or more away you can run south and get out of its way. Otherwise, find a ditch or stop in a store and tell everyone there to join you in the cooler. If you're not from tornado country it may sound strange to you to be invited by a store manager to hide out in their walk-in cooler, but here this is standard operating procedure. Don't hesitate to do it.
Can't think of anything else off the top of my head. Except figure out which way is south, which way is west, how to cover the window in your hideout room of choice quickly and effectively enough to at least slow broken glass down, and let everyone in on the plan. You really don't need supplies much; it'll be over in minutes. Just a solid place to put the first aid kit, mainly.
Now these are rules of thumb, and tornadoes do not obey rules. But though a little knowledge might be a dangerous thing, a lot of panic is far worse. So, if you've never thought it through, take a moment. And, hopefully, we'll stop exporting these things the way we've been doing the last decade or so...