Make friends with houseplants. They take in carbon dioxide and let out oxygen, and some varieties (like spider plants, English ivy, and bamboo palms) can even remove toxins from the air.
Keep it clean. Get rid of the dirt and dust particles that build up on the surfaces of, well, everything by vacuuming and cleaning on a regular basis.
Take off your shoes. If you don’t already have a designated area near the front door where your kids can put their shoes, make one. It will prevent dirt from being tracked in the house (and result in less time needed to clean).
Use an air purifier. They come in a range of prices, and are super effective at capturing icky particles. Try the Honeywell Pure HEPA Round Air Purifier, which manages to get the job done while being relatively inexpensive.
Groom your pets. Keep fur and dander at bay by brushing your dog or cat’s fur and bathing dogs frequently.