Last time I checked handguns needed to be shipped via overnight using UPS and MUST go to a FFL holder. Some receiving FFL holders require that you use a FFL holder to ship to them, but that is not required by law.
For more info, check out this website ->
http://www.thegunzone.com/ship-guns.html
In some locales, you cannot sell person to person without having a FFL holder get in the middle of the transaction (for a fee, of course), so check your local laws. If you have any local gunshows, that might be the best place to take the gun in order to sell it. Bear in mind that none of the dealers there will give you much for it. They will try to talk it down and make it appear to be worthless so they can buy it for a song and then put a high value on it.
One thing to bear in mind is that you cannot knowingly sell a gun to someone who is a resident outside of your state, and also that you would reasonably expect to be a felon. If you have never looked into it before, you will probably be bewildered by the number of laws you may be subject to now in trying to dispose of that gun.
Good luck!