It is a Federal crime in the USA for the following nine categories of persons to possess firearms:

  1. persons who have been convicted of a crime potentially punishable by more than a year
  2. fugitives
  3. users of drugs or marijuana
  4. mental defectives
  5. illegal aliens
  6. dishonorable dischargees
  7. renouncers of citizenship
  8. those subject to domestic restraining orders
  9. and those convicted of misdemeanor domestic crimes of violence

Title 18, U.S. Code, Sections 922(g) and 924(e) mandate a penalty of up to 10 years, and in the case of persons previously convicted three or more times of drug crimes and certain others, a mandatory 15 years to life with no parole.

Any person purchasing a modern handgun, rifle or shotgun from a retailer must sign an ATF Form 4473 swearing that he is not in one of these categories.

Lying constitutes yet another federal crime.

This is Federal law. Your State may have elaborated on these rules.