How do I find the static coefficient of friction of one car tire on a vehicle?

Static means the force to get it moving. The confusion factor is that four tires support the car, so you either measure the force to move the entire car and assume one fourth that much for each wheel, or you find some way to measure each wheel independently.

Another factor is that static friction is not the same in all directions. So you need to make a choice there, too.

The force to measure the entire car is no problem at all. The force on each wheel is a bit of a problem and you will have to invent something. I suggest you make four platforms that are hollow underneath. The hollow space can be very small. Am aquarium pump will inflate the hollow space enough to support the weight of the car. For example, one square yard of platform and one psi of air pressure will support the heaviest car and then you can measure forces to move the platform in the desired direction.

For more information go to google.com and search "air bearing".