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
It seems to me that there are a lot of such videos on YouTube and you could make your own air purifier according to the instructions. This will naturally take some time and you will spend a lot of effort on this case, which is why I recommend that you immediately contact Dehumidifier Critic which was very useful for me because I was looking for a quality air purifier and found this one. I used to think that cheap options are not always high quality but this website completely convinced me and offered several good options. I think you'll be interested in them too