Each state differs but generally you can find out how many points are on your license by obtaining a copy of your driving record or driving history. Most states require a fee to be paid before they will give you a copy of your driving record.
Some states will allow you to call into a special number to find out the points amount that your license number currently has attached to it. For example in Missouri you can call or email to find out the number of points. Arizona and Wisconsin will also allow you to call a special number.
To find out the number of points you have on your license or other information that might be on your motor vehicle record contact your state's Department of Motor Vehicles or similar agency.