Following someone in a car is not illegal unless you're stalking the person and seem suspicious as in you continue to follow that car at every turn and someone sees that your car is just the one following closely to that car.
But even then it's hard to get noticed as suspicious if you're following another car because many other cars and vehicles follow other cars and vehicles down the road which is legal.
But what would really be suspicious is that if someone was in a car and went down a back road and you continued to follow them or you continued to follow them around small streets everywhere they went then they might see you as being suspicious and call 911 to find out what is going on.
If you're not doing anything bad though then you won't get into trouble.
If you follow someone in your car just do not follow too closely and do not follow them down every road so as to not seem suspicious.