Doing a background check on a person for free requires knowing the full name and date of birth of the person. A free background check also requires you to know which states, counties and cities the person has lived in.
Most states, counties and cities offer free, online searches of government records. The federal government also offers some databases. To use these databases, you have to search each individual location's .gov website, locate the criminal records section and enter the name of the person being investigated. Some sites also require a birth date and possibly a Social Security number. Each website only offers information for that specific location.
It is also possible to request criminal records or a background check through local courthouses, although this might require a fee and permission of the person being investigated. Each jurisdiction has different requirements for in-person and online searches.
In order to access a full criminal record that covers all possible locations, it is necessary to pay for access to a private database via a website. There are records that are unavailable from any source. Records can be sealed by the court for many reasons. The most common reason for sealed records is because the offense was committed by a minor.