Research sizes of furnace filters and box fans before purchasing. You will want a box fan and furnace filter that have the same length and width. The box fan will be used to pull air through the filter. Furnace filters have an activated charcoal layer which catches particulates and odors. Get a furnace filter with a depth of one or two inches.
Build a frame equal to the dimensions of the furnace filter. Cut the 2-by-2 inch boards into four equal lengths. Nail the four pieces together to create the frame for the furnace filter. The furnace filter should fit snugly into the frame. If the filter is not airtight, use duct tape to seal any spaces.
Position the frame in front and flush with the box fan. Seal the gap between the frame and box fan using duct tape. If you want to use the box fan in other applications other than as an air scrubber you may want to use masking tape as it won't leave a sticky residue.