Is there anyway that a search can be done for someones license plate that can be done by oneself.?

You would have to start with the State Department of Motor Vehicles. Ask them what is public record and what they can tell you. Do you know the plate # and you are looking for the owner? Then you will need the DMV's help. If you know the person and want to find the plate # that would be easier-just ask what vehicles are owned by that person.