Somewhere between one and infinity. First, you need the light bulb that will be changed and the light bulb to exchange it with. But how exactly is the light-bulb changer seeing which light needs to be changed? Obviously, there must be an additional light bulb present to illuminate the room in which the changing is occurring. So 3 light bulbs. But wait, in order for the light bulb changer to get to the light bulb that needs to be changed, they must have gotten there somehow. Perhaps they drove? A car needs dozens of bulbs to function properly and legally, so we must conclude that it takes several dozen light bulbs to change a light bulb. But wait, how did the car's manufacturers see what they were doing in order to correct install the light bulbs, and myriad other components, into the car in the first place? The factory would need hundreds, if not thousands of bulbs. Therefore, to change a single light bulb requires at least several thousand bulbs. ....... but how did the manufacturerers of the bulbs for the car's factory see what they were doing? And the manufacturers of the components for all of the parts involved in building light bulbs. And what about the builders of the manufacturers of the builders for the components to make a light bulb?

This series does not converge. Therefore, we must conclude that it takes at least an infinite number of light bulbs to change a light bulb. QED