Remove the glass from the window where you are venting. Most basement windows are single-pane, hopper (sliding) style and are easy to remove. If a thermal window is in place, a professional should be consulted for removing this kind of window. To remove a single-pane window, scrape away any glazing with the putty knife. Carefully remove the window, using gloves to protect your hands.
Cut or have cut a piece of plexiglass the same size as the glass you removed. Cut or have cut a hole the size of the vent hose that you want to exhaust.
Obtain a vent kit appropriate for the size of the vent hole in the plexiglass. Install following the manufacturer’s directions. Typically these kits are used on other surfaces, such as wood, so you may have to adapt the screws. For example, you may need to use nuts and bolts instead since the screws may be too long for the width of the plexiglass. Use the existing mounting holes in the exhaust kit to mount the flange (and/or any other materials included in the kit such as a louver) to the plexiglass surface, using the appropriate screws or substituting nuts and bolts. Pre-drill the plexiglass so it does not shatter. Use a bead of caulking to seal the exhaust vent to the plexiglass to provide a water and airtight seal.
Reinstall the plexiglass into the window frame. If the glass was removed from a metal or aluminum frame, use glazing to secure the plexiglass into the frame. If the glass was removed from a wooden window frame, use wooden moulding pieces to secure the plexiglass to the existing frame.
Let the glazing set and dry over night. Attach the venting hose to the exhaust assembly.