One of the subscribers to a bicycle touring list that I also subscribe to recently got a flat (he lives in Florida so it's not too cold to ride) and he decided to let his LBS fix it while he made a video of the process.
I thought the video was worth posting. Probably because it almost exactly matches my method.
My notes:
I wrote to Ken (the bicycle owner) and noted that the mechanic talked about positioning the tire label by the valve in order to know where to look next time a flat occurred.1 However, the mechanic never performed that search with the flat being fixed. Ken said that because of YouTube limits, he had to edit the video and that the mechanic had spent about five minutes examining the old tube / tire.
I actually position the label opposite the valve. Presumably you can position the label anywhere as long as it is consistent so that you can use the label and valve to locate where the cause of the flat came through the tire.
Another member of the list noted that if the offending bit of metal or glass or whatever is not lodged in the tire but is loose inside, it will continually roll to the bottom as you examine the tire so you ought pay particular attention to that. I've added that to my procedure.
I pump up the tire maybe a 1/3 to 1/2 way and examine the bead seating as in the video. I also knead the tire as you can see. I also might bounce the tire on the ground in a couple places. After that, I deflate the tire again in order to relax the inner tube. My theory is that if there were kinks or creases, the now relaxed inner tube allows them to straighten out.
1 When the next flat occurs, you pull off the tire and find the flat in the inner tube. Once you find the puncture, you know to look at the tire the same number of degrees away from the label as the puncture was from the valve.
