I've been a fan of and involved in drag racing since I was a kid. So that has made me very familiar with how things go down and I know what to look for.
One thing I do is to keep both eyes open and I watch the tree (starting lights) with my left so I can anticipate when the cars will launch. I also try to focus my attention to a specific point on the car - like where the A pillar meets the door - and keep that at the same point in the frame as the car moves.
Like many other types of photography, being prepared is important. I pick which car I want to shoot and brace my leg against the bleacher seat in front of me before the cars are staged. I may make a couple of practice rotations to make sure I'm steady and can follow the action for as long as I need to get the shot I want.
Although it didn't work out in the shot of the Super Sport, I had positioned myself so I could catch the cars as they passed under the NHRA banner like in this one: