It varies in each State how you go about reporting an individual that you are aware of that is driving a vehicle without insurance. In most States if you contact the local Department of Motor Vehicles they can direct you to the correct state agency to report the uninsured driver.
No matter what State you are located in, if you know of someone whose vehicle is uninsured and yet it appears that the DMV has not yet been informed, you can try to report that vehicle owner to them. Typically the DMV has a consumer hot-line that you can call into to ask questions or report problems. They might be able to take the information or forward you onto the Financial Responsibility Unit or other appropriate state agency.
For example Florida has a Bureau of Financial Responsibility and New Hampshire's' Division of Motor Vehicles has a Financial Responsibility department which has its own insurance information phone number to call.
The DMV or other state agency will tell you what information you will need to provide to them. It is likely going to be the name, address of the person and perhaps also information on the vehicle such as the license plate number.