In order to run a free background check you need some basic information about the person you are investigating. More information you have better the chances of getting accurate information. The most common information used to search and get background checks are name, last name, city and state the person has lived in. If you have exact addresses even better. Of course more information and you get the person accurately identified, so probably the most accurate will be if you have a SSN or social security number where only one number per person is only issued. Free background checks are not exactly free. Since you are doing most of your research then you are not spending any money on getting the information it is more time consuming and keep in mind even some government agencies in some states do charge specially for providing criminal informaiton.
Free Background Check by State
Also keep in mind different jurisdictions have different rules about release of information. You also have restrictions in terms of readily availability of data. Not all states, counties and courts are computerized and sometimes it is very difficult to get to all the data you need. That is sometimes it is more popular to use online services who provide you a report based on public data researched and ready by special data providers. But if you choose to do your own research below you will find information as to how to research and get background information on anyone.