Obtain the total number of fuel sales for retail gasoline and diesel for the given area. To find out these numbers, you should contact your state's Department of Transportation. They will likely have a traffic data branch in charge of acquiring these numbers.
Multiply this number by the miles per gallon, which is the miles traveled per gallon of fuel purchased. Again this information will have to be obtained from your state's Department of Transportation.
Divide this number by the unit price per gallon of fuel in the area you are calculating. The total will give you the VMT. The number you are looking at should be an estimation of the fuel price per gallon in whichever area you want to examine. You should keep the area constant when looking at the total retail sales of fuel. VMT can be used to calculate vehicle miles traveled in one state, in the whole country or just on one specific highway.