For the OP its fairly simple as far as NC goes. Federal law has said that any transfer of a pistol across state lines needs to go through an FFL, with a couple of narrow excpetions I have heard of, which I myself would not be comfortable doing, but thats just me.
If you want to go through with this, you find a FFL or Gunshop in your area. If you would give us an idea where in NC you live, myself, or others should be able to point you to a gunshop that can help you with this.
Step 1. Go by your local Sheriffs Dept. Apply for a pistol purchase permit. should take about 5 min and a few bucks. I think the cost and the actual application still varies alittle by county. All they are doing is checking your criminal background. You may have to fill out the form and drop it off one day, then pick up the permit another day or so later.
Step 2. Find arrange a local FFL/Gunshop to recieve the pistol when your grandfather has it sent to the FFL/Gunshop. This same FFL/Gunshop will handle the paperwork from there.
Step 3. When the pistol has come in to the FFL/Gunshop, you stop by, fill out the 4473 form, and the FFL/Gunshop will do a nics check to check your background once again. You will also give the FFL/Gunshop the pistol permit you got from the Sheriffs Dept. If the nics check is clear, your good to go, and you take the pistol home after paying the transfer fee, usually around $25, but ask first when you talk to the FFL/Gunshop.
Exception for Durham County
Step 4. After you pick up the pistol you must register the pistol with Durham county gov. Since I live in another area of NC I do not know what they require, but the durham county website AFAIK did have it listed.
Hope that this clears things up for you. Enjoy the gift!