One of the consequences of a felony conviction is the potential to lose your rights to own or possess a firearm. Whether you can get these rights back depends on where you live.
Each state manages its own laws concerning felony consequences and the ability to restore rights. According to the Restoration of Rights Project, you do not necessarily lose the right to own a firearm in Washington DC, but you lose the right to qualify to register a firearm, which is the only legal way to own one in this area.
Before worrying about restoring your rights, you should ensure you lost them. Felony conviction usually leads to a loss of rights, but it must be a certain type of felony. If your charges relate to weapons, drugs or violence, then you probably did lose your firearm rights. In addition, if the court deemed you a chronic alcoholic or found you innocent by reason of insanity, then you also may lose your rights.
The state does not have any method by which you can restore your rights after losing them except by pardon. There is an exception if the court deemed you a chronic alcoholic or you had an insanity acquittal. In those cases, if you can provide medical proof you no longer suffer from the condition, then you may have your rights back.
Getting a pardon is very difficult and rare. You would need to get it from the President of the United States. To do this, you must go through the Clemency Board first and then have the president choose to give you the pardon.
In Washington DC, it is hard to get your firearm rights back after you lose them, which is another motivating factor for some people to avoid a felony conviction if at all possible.