First things first: Resin is very aggressive. It can very easily make you hypersensitive, even to the fumes of it. So step 1 is easy:
Wear gloves when working with resin. As you live with your printer in the same room, bottle up the resin right after use and only open it during use to prevent buildup over time and exposure. To further reduce the exposure, leave the room while printing if possible and ventilate the room after bottling the resin again. Possibly even wear breathing protection during operation.
Enclose and seal the machine
To keep the vapors away from you, the machine needs to be enclosed airtight. Any lids need to get a seal, non-opening joints of the frame need to be sealed with a sealant like silicone. Often it is hard to retrofit an enclosure to seal up the workspace.
If you want to enclose the full machine, I suggest using glass sheets and silicone sealant for the whole inside. Brace the construction from the outside with L-profiles along the corners and joints. The most tricky part will be the opening hatch and wiring/ducting access hole. The opening seal needs a sealing lid all around that gets compressed on closing the machine up and some kind of lock to keep it this way. The air filtration and wire access are just hard to make because of their circular shape. You might want to use a wooden or metal base plate, so it is best to put ventilation through the base. In case of wood, afterward coat the inside surface with a thin layer of an airtight material, such as epoxy resin or silicone.
Low presssure operation by ventilating the machine
The next best thing to isolating the machine workspace from the air completely is to make it a low-pressure operation. This means that you evacuate the air from the machine. The imperfect seals now work against a high pressure outside and low pressure inside, meaning that the flow in any non-sealed spot only knows one direction: into the machine.
Fred's answer provides good basics on how to do this in general by using parts for Laser evacuation. This is also the most space-economic way.
But there are (partial) indoor solutions even, based on ventilating the air from the printer into a multi-stage air filter could reduce or eliminate the amount of chemical exposure. This is not a slim piece of foam, it is a boxy setup with about 3 to 6 stages of filtering. Among dry-filters, a paint-filter in combination with an active coal one should eliminate a large portion of irritants from the stream, but might still need to be vented outside to reduce exposure even more. A 'wet' air filter, where the exhaust of the machine is pearled through a basin of a cleaning liquid (often water or a solvent like isopropylic alcohol) like in an aquarium could help to catch even more chemicals but is bulky.