I usually just replace a tube once it is punctured, but it is a good skill to know how to patch a tire on the road. I am always amazed how many riders can't replace a tube, let alone patch one. I flatted both tires once (glass in the road hiding in some deep shade). With only one spare tube and no cell phone coverage, you want to know how to use a patch kit.
Take the flats home and practice. It is bound to happen eventually...