In most cases, you can look at the tire size identifier on the sidewall to determine how old it is. Some tires may also have a DOT code that has a letter and number combination; this stands for Department of Transportation and shows when the tire was made.
If these codes do not exist on your tire, then you will want to look for the DOT number which acts as a guarantee that it is safe to use on your vehicle.
If you are unable to determine when the tire was made, you can always contact the manufacturer directly to inquire about its production date.