I used to hook up my spraybooth through a dryer vent that went out the dining room window. I used a sheet of 1/2" MDF, cut the hole for a regular dryer vent and sized the panel to fit in the open window. A few strips of weatherstripping (not seen in the photo) and voila!
The smaller board was used to friction fit the panel into the window so it wouldn't fall out. Boy, was my wife ever glad when I got my man cave set up and moved the booth downstairs!