Yes to buy a gun you have to pass a background check first which can take a few minutes to a few weeks.
If nothing bad comes up on the background check then you should have no problem purchasing the gun.
However there is one work around and that is if you buy the gun at gun shows or from an individual.
Most states don't have laws that say that gun shows or an individual has to perform background checks before selling a person a gun.
The background check law only goes for licensed gun dealers at gun shops.
You do not need to undergo a background check if you purchase a gun online, through a gun show, or through private sales.