Great find! How fun. You do indeed have a vacuum coffee maker -- a.k.a. vac-pot, syphon, or siphon.
This style of vac-pot is intended to be used on a stove-top (specifically: having a flat bottom, and with a handle on the neck of the bottom part -- the "bulb") -- looks a lot like this current model from Bodum - c/o Amazon. There's a good primer on the history and types of vac-pot at WeCraveCoffee with some good pictures.
However, in general, glass pots are generally not recommended on flat glass-ceramic cooktops for a couple of reasons: they can scratch or otherwise damage each other, and the poor conductivity of glass makes glass-on-glass heating less efficient. More info on this from a question on Seasoned Advice, and recommendations from GE Appliances for their own stovetops. I did see some products such as this one that depicted glass vac-pots on glass-ceramic cooktops. If all of the glass is high quality, as should be expected for cookware intended to be used on a stove, it should be able to withstand the temperature changes induced by a cooktop. I (personally) would be comfortable using this vac-pot on a gas flame, but cautious/wary of using it on glass-ceramic cooktop. Glass cookware works well over gas flame, but I have less experience with glass cooktops... your "mileage" may vary.
For a more "DIY" adventure as you suggest, consider a mechanism to suspend the vac-pot over a flame heat source. Other styles of vac-pot (such as this Hario model - c/o Amazon) have a scaffolding that holds the bulb (bottom) and the hopper (top) so the whole apparatus can be suspended over a separate heat source, like an alcohol or butane stove. Check some vac-pot brewing guides that show this type of integrated round-bottom bulb and holder (e.g., from Blue Bottle, Stumptown, CoffeeGeek, and many others). Warning: this may remind you of Chemistry lab from School. ;-) And of course be careful with fire.
Separately, just for completeness...
It also looks like you're missing the filter piece. These are inexpensive (relative to the whole apparatus) and you'll want to purchase a new, compatible one anyway (see also another question on siphon filter replacement).
Another thing you'll want to check is that the rubber seal between the bottom and top parts is still in good shape, especially if this pot hasn't been used in a few decades. This is for reasons both practical (you need a tight seal for the vacuum to work well) and safety (you don't want the seal to come lose and spray boiling-hot water everywhere)!