To get a shot like that, choose the spot on the track where you want to capture the car. Set your camera on manual focus and pre-focus on that spot. Set-up your shot, so your lens is at the mm you'll have it when shooting (try a few dry runs as cars go by, just to see how wide you need to be). Then, look at your lens and see what mm you're set-up at. Set your camera's shutter speed to a speed that's roughly equivalent to the effective focal length of your lens (meaning, if your lens is set at 150mm, try a shutter speed around 1/150th or whatever's closest to that). When you're ready to shoot, set your feet apart at about shoulder width and face right toward where you're going to be shooting. Twist your waist and point your camera to where the cars are coming from. Look through your viewfinder and pick up the car you want to shoot (don't refocus! Let it be blurry here) and follow it as it moves toward your focus point, turning only with your waist (don't move your whole body). As the car enters your focus area, snap the shutter and KEEP MOVING YOUR WAIST, so the camera continues to move along with the car. Follow-through is extremely important in this case!! This is much like a golf swing. After your follow-through, take a look (assuming you're shooting digital) and see if you got the shot.
This is a technique that takes practice. Slower cars are easier to catch (like vintage race cars). I've tried this with Champ Cars at full speed on ovals and I'm simply not fast enough. I can sometimes do it on pit lane, but not always. But, with vintage cars, I've done literally hundreds of really nice panning shots. You'll need to shoot A LOT of photos to get a few really nice ones. Just keep trying, keep shooting, and you'll come up with something.
And that photo in the OP's message is most likely NOT a Photoshop. A good, experienced motorsport photographer who specializes in action shots can do something like that. I see it all the time.