Any private party seller may sell you a handgun (assuming you aren't a convicted felon ), and you may OC the same as everybody else.
I'm not going to provide cites because it's difficult to cite laws which don't exist, such as any in Virginia addressing the carry of handguns for 18-21 year olds. (I.e. there are none.)
As for the process of buying private party, there really isn't one. Find someone who wants to sell you a gun. Check http://www.vaguntrader.com. Meet up, buy the gun. Cash & carry.
No special procedure needed. You don't even need to keep records, although it might be a good idea, depending on your perspective.