The normal method is to use a corona discharge to charge the dust particles.
See wikipedia extract below.
I'd imagine that using a DIY negative ion generator would essentially accomplish the same result - and there are many designs avilable on-web.
Many negative ion generaotors here including circuits.
eg Here is an off mains diode / capacitor voltage multiplier.
This will kill you if you let it.
This one starts from 12V. It can still kill you.
Very practical looking DIY page here
Bad hair day - ion emission head.
Lots of detail
Smalle than it looks above:
The plate precipitator
The most basic precipitator contains a row of thin vertical wires, and followed by a stack of large flat metal plates oriented vertically, with the plates typically spaced about 1 cm to 18 cm apart, depending on the application. The air or gas stream flows horizontally through the spaces between the wires, and then passes through the stack of plates.
A negative voltage of several thousand volts is applied between wire and plate. If the applied voltage is high enough an electric (corona) discharge ionizes the gas around the electrodes. Negative ions flow to the plates and charge the gas-flow particles.
The ionized particles, following the negative electric field created by the power supply, move to the grounded plates.
Particles build up on the collection plates and form a layer. The layer does not collapse, thanks to electrostatic pressure (given from layer resistivity, electric field, and current flowing in the collected layer).
Wikipedia ref here - press Esc when page appears to prevent the black screen of SOPAR.