I'm new to road cycling too and as I posted elsewhere, was lucky enough to have my first flat at home! Walked in to the garage to get ready to ride and there it was. Had never changed one before, but I had just watched several instructional videos on Youtube, and it only took me a half hour or so, and that included my essentially doing it twice (same new tube, but as I was nervous about it, I got it done and took it apart again to check it all out thoroughly). I also, after the suggestions of others here, carefully looked for the cause and indeed found a teeny piece of glass in the tire that clearly would have eventually caused another flat--sooner than later I expect. This was a front tire though---the back does look trickier.....I think I will check out my LBS or REI and see if they have some maintenance classes---I like to be self-sufficient.

(As for falling over, I'm afraid of that too--if I injure a hand or wrist I literally can't work. I've elected to ride platform pedals on my road bike for that very reason).