Here's one made from a box fan, and two air filters! https://www.popularmechanics.com/home/how-to-plans/how-to/a21300/diy-air-filter/
Some people cut furnace filters and put them between their air vents and the floor on each vent. This does not clean everything, but it helps. They need to be rinsed off at least once a month.
activated charcoal and news paper are air purifiers
A box fan and an a/c filter is a simple air purifier