First check and make sure that you have a legitimate reason for needing to conduct a search on the license plate. Researching a license plate must comply with the Driver's Privacy Protection Act (DPPA). Unless you are a member of a governmental agency, an insurer, an employer, or a licensed private investigator, it is only permissible to research a license plate for uses related to matters of motor vehicle or driver safety and theft.
File a request with your state's Department of Motor Vehicles. After proving you have a legit reason for needing this information, you will need to fill out a form stating that your need fits the law and pay a small fee.
Check an online database such as Abika or BestPeopleSearch. Unfortunately, services such as these are not free so be prepared to pay a fee. Once you have access to a database, simply enter the license plate number and the online database will display any stored information about the vehicle and its owner.
Hire a private investigator. Although these investigators also charge fees, they have access to a number of resources that can help research the license plate number and promptly get the information back to you. Check online or in your phone book's Yellow Pages to locate a private investigator in your area.