Measuring Dust Concentration in Air

Google Air SPM Measurement or Counters and you will get link to any number of suppliers including cheap, handheld ones.

As far as making at home, I am not sure.

To build a state of the art device would be a challenging project that would bring together all these components: Calibrated flow nozzle, light source, light scattering device, a photo multiplier tube, and an electronic counter (I'm leaving something out?); all arranged in some type of housing that would make it not inconvenient to use. You would also need some NIST traceable standards to calibrate the gizmo.

or,

You could go primitive by making a large piston type suction pump or something that you can use to draw a known volume of the air to be sampled across a filter paper. Then you can count the particles trapped on the filter under a microscope.

Yes, there is a standard white board with many squares. You count both the average number of particles on the board and the percentage of area covered by the dust.