IMHO the best approach is to use a 'hobby knife', an aluminum Exacto blade holder with the acutely angled #7 blade is about as good as it gets. The handle is light and round so it 'twirls' between the fingers nicely.

Using only the weight of the knife itself spin the knife and drill down through the nail. With a new blade, properly sterilized of course, it only takes a few turns. As soon as you hit blood stop. Relief is immediate and the drilling process is painless with only a slight twinge as you hit the live membrane under the nail. Press up gently from the pad of the thumb to make the hole bleed. Clearing the clotted blood and washing out any particles from the drilling. Smear a bit of neosporin on the hole and cover with a band-aid.

I have used the hot paper-clip. It gets through the nail but can cook the meat and make the damage worse. I have also used a drill with a fine drill bit. This too works but you need to watch the depth. It is easy to drill through the finger. Making the problem far worse.

You can use any sharply pointed tool to drill the nail. The pointed tip of a pocketknife will work. Some traditionalists simply place the tip on the nail and push it on through. One guy I know taps the blade in with his hammer. Both methods work but are IMHO far too painful, brutal and potentially damaging to re