I have been plugging my own tires on my cars and trucks forever. Plugged a tire or two in Iraq too. Never had an issue with a plug repair...ever. I even had a triangle piece of metal in a 37 on my Ram, took 2 plugs to get it to stop, wheeled the rest of the day on the tire, then swapped the spare on to drive home.
I had 2 nails to plug on my old wrx, went another 20k on the plugged tire without an issue.
Only plug the tread, never the sidewall. I don't even mess with a puncture on the shoulder of the tire, just too questionable.
Get a plug kit at the auto parts store or even walmart. Air the tire up to about 10psi to make it firm. Pull the nail out with needle nose pliers. Use the reaming t handle to clean out the hole. Put plug in plug tool and coat plug with rubber cement. I usually put some rubber cement on the edge of the hole too. Push plug about 2/3 into tire and then pull tool back out. Plug will stay in tire. Use razor blade to cut excess flush with tire and air up. All fixed.