Check to make sure your dryer is venting outdoors. A loose hose connection or gap in the dryer vent allows moisture to seep into the basement.
Add caulk to a caulking gun. Caulk around basement windows and doorways as needed to seal tiny openings that allow humid air to enter the room.
Close all basement windows and doors. While you might expect open windows to help remove excess air moisture, open windows allow humidity to come in from the outdoors.
Run an electric fan to circulate the air. Air that's stagnant and heavy in the basement keeps moisture in the air. Point the fan toward the basement steps to allow moisture to escape upstairs.
Control the humidity level with a dehumidifier. Check the water tank often to empty it out and keep the dehumidifier running.
Wipe up spills from a basement laundry room quickly with cleaning cloths. A small amount of water on the floor may seem inconsequential but ends up evaporating into the air.