Zippos are very complex. In short, the flint wheel is moved causing a spark in the wick. The tube passing all the way from the inner part of the zippo to the wick contains the fuel used for the zippo's ignition. When lit, fuel is constantly passing through the previously mentioned tube at a slow rate - burning slowly. Due to the nature of the zippo's fuel, this whole process is very slow which is in fact good.
Though this might seem simple to accomplish, it must be noted that a zippo contains more than 22 pieces (modern zippos contain up to 40 pieces). To make a zippo, more than 110 manufacturing operations are needed.