How to Conduct a Background Check for Firearm Sales Between Individuals
Any person may sell a firearm to an unlicensed resident of the State where he resides as long as he does not know or have reasonable cause to believe the person is prohibited from receiving or possessing firearms under Federal law.
Typically, when a person sells a firearm on a classified ads website they will have no way of knowing whether the buyer is "prohibited from receiving or possessing a firearm". Legally we are allowed to sell a firearm without a background check. However, the moral and possible legal reprecussions would be serious if that firearm were used in an act of violence.
Here's an incomplete list of people who may not possess a firearm:
Fugitives from justice
Persons convicted of domestic violence
Persons who are covered under a protective order
Unlawful User/Addicted to a Controlled Substance
Adjudicated Mental Health
Persons who were dishonorably discharged from the military
Those who have renounced their citizenship
How can an individual seller perform a background check on a buyer?
There is no public access to federal criminal background databases such as NICS. Therefore, it is not possible for an individual citizen to perform a firearms background check.
The NICS system or National Instant Criminal Background Check System is a database maintained by the FBI. The purpose of the NICS system is to provide federally licensed gun dealers the ability to execute background checks on buyers to verify their eligibility for gun ownership. If a seller wants to perform a background check they will require the assistance of a licensed firearm dealer or manufacturer.
How do I find a FFL to do a background check?
Contact a local gun shop and ask if they would be willing to do the background check for a person to person transfer. Most will charge a fee for this service. These fees can range anywhere from $15 to $50+ so it's worth your while to call around. Try to support a locally owned shop whenever possible.