A good idea might to have the LBS fix the flat and ask if ou can watch them do it, thereby gaining some "ed-u-ma-kay-tion" about the process.

As a side note, beyond carrying a pump, spare tube, and patch kit, I'd add a pair of throw-away gloves to keep your hands clean while changing out the rear tube, 'cause it seems like the rear tire goes flat at least 3 to 1 over the front tire. I got a box of vinyl gloves at Stuff-mart. I think the box was under $9.