The act of adding a driver does not usually cost anymore. It may cost more to add a driver to your policy if that driver is a higher risk or exposure, since your auto insurance is taking on the risk of this person operating your car. The driver's motor vehicle record (MVR) will be looked for rating purposes and then if there is a cost to add the driver your insurance company should inform you.
If you are a young driver and you add your parents who have no tickets, it will likely cost nothing more. If you are a parent and you add your young driver to your policy, it will likely cost more to insure them on your policy.
In general, insurance companies do not rate insurance premiums on the amount of drivers. They tend to rate the highest risk driver with the highest risk vehicle.
Insurance companies' guidelines vary so it will ultimately depend on the rating system of the auto insurance company you are using. Anyone that lives in the household or uses the vehicle occasionally should be listed on your policy as a driver normally.
It depends on the insurance company and their guidelines as well as their rating systems if it would be cheaper to have someone listed as an occasional driver or primary driver on your vehicle if you are trying to decide how someone should be listed on the policy.
Regardless of cost, you will need to tell the use of the vehicle by the person as defined by your specific insurance carrier. So speak with your insurance agent and see if your carrier has different types of driver designations and how they would advise you to add the person you are thinking about adding as a driver to your auto insurance policy.
Your agent will be able to advise you about your insurance provider's rating system and if your premiums will go up if you add this driver to your policy.