How do you go from the old tire measurement system to the new one?

I'm not sure which measuring systems you are referring to. The one used most commonly today is like P235/75R15. P is Passenger tire or LT for Light Truck Tire or ST for Trailer Tires. 235 is the width of the tread in millimeters. 75 is the height of the sidewall as a percentage of the tread width. (So the the height of the sidewall is 75% of 235 in this example.) R is for Radial tire construction. 15 is the diameter of the hole in middle of the tire. It should match the diameter of the wheel that the tire is mounted on.