Many different things can prompt a person to want to search for another person. One of the ways to find someone is to look up his vehicle tag number. The process of looking up someone's tag number is not terribly difficult, but you will require a legal reason to look someone up using his vehicle tag. Under the Drivers Protection Privacy Act, it is only permissible for a private person to look up another citizen's information using his vehicle tag information if "in connection with matters of motor vehicle or driver safety or theft". News media, businesses, and other organizations can look up a person's information using his vehicle tag information for a number of reasons. If you have proof that you are researching this person's information for one of the allowed reasons (for example, in the case of a hit and run), then you are legally permitted to use that person's vehicle tag to look up his name and address.
The process of looking up someone by using his tag number is going to start by going to your state's DMV website. You are then going to have to go through a couple menu options to find the exact one that you want. Since this is not a feature that the general public can use on a whim, some state DMV sites don't have anywhere that you do this online - you may have to use the 'Contact DMV' option.
For those states which do allow vehicle tag lookup online, look under the menu tab and then choose 'Driving or Vehicle Records' or any similar option. You must follow the directions on the site to the letter, or your request will be delayed. For most states, you will need to fill out a record request form and verify that you are seeking the information for a legally permissible reason. You may need to provide proof of such a reason (for example, an insurance claim or police report). This requirement helps prevent disgruntled employees or stalkers, for instance, from discovering personal information about their intended victims. Most states require a small processing fee (often under $10) to locate these records. Once you've applied for this information, be prepared to wait for one to four weeks. You will usually receive the information in the mail. In some states, you can request certified copies for your insurance company if necessary.