Puncture repair kit

Do you carry one? Which is better? How do you inflate a tire when you're out on the road?

I'm asking because I'm new to this. So far, I've only ever used a small 110 cc bike to crawl around the city. Flats are no problem as there are always a repair shop just a push away. But I plan to take my Icon Red on longer jaunts in the country and I'd like to be prepared.