I have kept a tire plug kit with me on every vehicle I have owned since I was 16 years old and learned how to plug tires while working at a Goodyear tire shop. Almost forty years later, I still plug tires and have never had a problem. I can't count how many tires I have plugged for friends and total strangers.
As was mentioned earlier, sometimes the hardest part of the job is extracting whatever is in the tire, but if you have a screwdriver, side cutters and Channellocks, you should have all you need for extraction.
This is the kit I am using right now. It is made by ARB and it is heavy-duty -- it will not bend while doing its job like the one "The Wynns" show. Don't cheap-out on this tool.
Bruce