Filters- Some air purifiers clean the air by having it pass through a filter to remove odors and airborne particles.
These are sometimes called air cleaners. In households, these filters are usually part of the heating or cooling system and are only effective when A/C system is running.
Ionizing Purifiers- These air purifiers use a method called corona discharge to create charged molecules called ions.
The corona discharge is a small but intense electrical field. Molecules passing through it will pick up an additional electron, giving the molecule a negative charge, the negatively charged particle are electrostatically attracted to the airborne molecules with positive charge. (like a magnet)
Ozone Generators- An ozone generator works much like an ionizing purifier, but it is designed to alter molecules of oxygen and turn them into ozone, a molecule made up of three oxygen atoms. While most of this oxygen recombines into dioxygen, some atoms create ozone. Home should be vacated, during treatment.
Adsorbents- Many purifiers incorporate an adsorbent material to soak up odors, fumes, and chemicals in the air.
Adsorption (not absorption) is the process of one substance adhering to the surface of another substance. The most common adsorbent is activated charcoal, which is very porous, and the larger particles become trapped in the many pores in the charcoal.
UV Light- Ultraviolet radiation renders certain micro-organisms sterile (and harmless). Some air purifiers feature a UV light that bathes the air as it passes through, eliminating the potential harm of airborne bacteria and viruses.
All the above purification systems require electricity, cleaning, filters and are only effective when running.
The following links will provide you with additional information on indoor air purification products.
6 Best House Odor Eliminating Products
Removing Odors While Painting
5 Ways To Make The Air In Your Home Healthier