Zeolite is a mineral, you get a bunch of small pellets of it in a bed, and run air over it while cooling it. The CO2 (and H2O) stick to it while everything else goes over it. Once you're at capacity you vent it to space and heat it, the CO2 (and H2O) leave the bed (into space) and recharge it for the next cycle. Repeat forever.
The consumables here are the small amount of gasses sent overboard, and energy, nothing else.
(And you use multiple of these beds because capturing CO2 is exothermic, and venting CO2 is endothermic, so you want to run a heat exchanger between the two beds in opposite cycles to minimize energy usage)