In order of the residents to not choke to death on their own carbon emissions, and to prevent fouling of electronics by water vapors, the air must be scrubbed. (this one was written really quickly and I haven't quite finished the main body on why everything needs to be done)

Solutions: (I really need to see if I can't figure out some more futurey solutions for this, because these are all things we can do right now...)

Chemical Scrubbers - Capable of clearing the CO ₂ and H₂O out of the air through chemical reactions with in the scrubber. Carries the added bonus that most scrubbers are designed to remove other toxic gasses from the air supply. Because all a scrubber does is remove other gases to keep their levels down, you must still have a way to regenerate the oxygen supply.

Electrolysis of Water - By running a current through water you end up with both hydrogen and oxygen as pure gases. The oxygen can be fed into the atmosphere, while the hydrogen can be fed into a the fuel system for a fusion reactor, saved for reaction mass, saved for station keeping or maneuvering jets, or just vented straight into space.

Photosynthesis - If the ship or station is growing plants to either supplement their diet or to provide the totality there of, the greenhouses are likely converting enough carbon dioxide into oxygen to negate the need for more complex solutions.