I realize your question is about what you should do AFTER you get a puncture. Most folks have already covered that subject well. With the hope that I'm not hijacking the thread, let me talk about what you might do to greatly reduce flats.
While riding my last bike, I got tired of rear tire punctures. (I've heard the theory that the front tire flips to nail up, then the rear tire hits it when the point is up.) When I replaced the rear tire a second time, and both times I replaced it with tread to spare, my independent tire dealer recommended I have Ride-On installed.
http://www.ride-on.com/motorcycles.html I did so, and I didn't have another flat with that bike.
When I bought my NT new, I had a flat on the rear after only 3,000 miles on the bike. Grrrr - and it was in the area where the sidewall meets the tread area. Once again, I had Ride-On installed with the new tire. Just the other day, I had a new PR4 installed - the tread almost gone. I had noticed air pressure loss of about 3-4 pounds after a 400+ ride back from Houston. Normally, there is very little air loss with Ride-On. (I check tire pressures weekly, and daily on long rides.) As I waited for the technician to finish with my tire, he came out into the customer area - and with a grin on his face asked if I was installing a new tire because of the lack of tread in the old tire or the nail in it. Sure enough - there was a small nail in the old tire, right where the sidewall meets the tread area. Technically, Ride-On should not have prevented a flat because of the location of the nail, but it did hold because there was a fair amount of Ride-On in the area where the nail penetrated.
True - the stuff is not cheap, but I recommend it highly. It goes into every new tire I put on my bike in the future.