[LittleChief]

Definitely close the windows and doors to the outdoors.

Many people will install a dehumidifer(s) in the basement. There are portable units that cover a relatively small area and you have the water discharge issue which can be piped to a floor drain or to a tank. Large dehumidier units are made that run in the $1000 area which might help for the entire space. It depends on your situation.

Assumptions: No HVAC for basement space and running duct lines will be relatively simple above the ceiling (if there is a ceiling).

My suggestion is to look at the small supplemental HVAC units depending on the square footage involved that are made for porches, sunrooms, new additions etc. and have one installed. It will function just like a regular central HVAC unit. You will probably have to run some duct work to the various rooms in the basement. Run fans too to keep the air moving.

Or you could enlarge your present HVAC system to include the basement space.

Another option is if the space is not heated or air conditioned is to essentially install vent fans in the foundation wall and keep those running to discharge the cooler humid air. Having the intake at the base of a wall where the coldest air is normally present can be done with flexible pvc pipe secured to the vent fan.

Shoot for 50-60% humidity.

Hope this helps.