As requested, my plugging 'technique'...
I get my rope set in the t-handle. I then get the reaming t-handle (the one with the sharp pointy end) in one hand and a pair of pliers in the other. I pull said offensive item out of the tire and immediately insert the reamer to prevent losing too much air. I'll ream the hole by going in and out and also rotating simultaneously a few times. When that is finished, I'll remove the reamer and immediately start inserting the plug t-handle. It usually takes some gumption to get it in there. I'll insert until about an inch, inch and a half of rope end is sticking out, then I'll remove the handle. Lastly, I'll use a razor blade to cut the rope ends off about an 1/8-1/4 of an inch above the tread. Then I ride as if nothing happened.
Michelle, welcome! I've been to Australia and absolutely loved every minute of it!