The antenna is a one piece assembly, consisting of the antenna itself - that is the part that is above the cowl and is visible. Connected to this is the antenna cylinder, which is to the left of the car - below the cowl and under the dash, so this part is not easily visible, but can be located by following the small vacuum hoses if they are still intact. The antenna cylinder has two vacuum ports - one near the bottom and one near the top. Removing the entire assembly is not easy - I have heard that in some cases it is necessary to drill a hole in the floorboard to allow the assembly to be removed by dropping it down through this hole (with car on a lift). I recall that when i removed mine, (not wanting to drill a hole in the floor) cut out a section of a flat metal support along the inside behind the driver's kick panel to remove the old antenna and to install the rebuilt one. It is then possible to wiggle the assembly down and out of the car, but it is not easy. An ample supply of band aids is a good idea. I later screwed a patch over the section of metal that I removed to accomplish this. Not a big deal as it does not show after the kick panel is replaced.
UP: The way it works is that when you push UP on the knob to the vacuum control switch, the vacuum is diverted to the UPPER port of the antenna cylinder, which receives vacuum and pulls the antenna into the up position.
DOWN: When you pull DOWN on the knob, the vacuum is diverted to the LOWER port of the antenna cylinder, which receives vacuum and pulls the antenna into the down position.
When vacuum control switch is released, the antenna stays in whatever position is desired (up, down, or part up or down).
When working properly it is remarkable how smoothly it operates, but as Doug said, these are prone to problems as they age. I often wondered if some WD-40 could be sprayed into the ports on the antenna cylinder to give it a little lubrication, but this might not be a good idea, so will defer this thought to others.
I also seem to recall that the center barb of the vacuum control switch is for the main feed of vacuum from the engine. If switch does not work as described above, simply reverse the upper and lower vacuum hoses on the side of the switch, which can be reached easily while laying in an upside position and reaching up under the dash.
Fred