Measure the box fan frame to determine the picture frame, or vice versa. The picture frame should be the same measurements as that of the box fan. When placing the frame on top of the box fan, the rim of the box fan should overlap with the main width of the picture frame.
Affix the wooden frame to the back of the box fan using super glue. Run a line of glue around the rim of the box fan's back, then press the frame face down on to the box fan's rim. It is important that the frame is glued onto the box fan on the side where air will be sucked in, rather than blown out. Allow it to dry overnight.
Seal the edges of the frame with epoxy. Once the frame and fan are permanently affixed, squirt a line of sealant epoxy along the entire seam between the frame and fan. This will not only reinforce the old, but will help seal air from leaking out, reducing the efficacy of the final filter system.
Glue strips of Velcro to the frame. Now that you have the wide inner rim of the picture frame to work with, there should be plenty of room to put down the Velcro. Use the rougher "hook" texture of Velcro, and glue it down to face outward.
Stick the furnace filter on to the Velcro. The furnace filter will already have a rough cloth surface, causing the Velcro to instantly stick to it. You should now have a furnace filter semi-permanently attached to a frame which will guide air being drawn through the filter and into the box fan.
Operate the fan as normal. Use in any room of the house. The furnace filter is unlikely to affect the fan's overall performance, but will bring a notable difference in air purity. Air sucked through the fan will have its contaminants filtered through the furnace filter, producing a high output of clean air.