Remove the Source
Removing the source of a foul odor is the best home remedy. This may sound obvious for garbage stinking up the trash can, but sometimes the precious wool quilt that grandma knitted might get soaked with spilled milk and start to stink.
If an item cannot be cleaned or treated, throw it out or put it into storage.
Charcoal or Baking Soda
Put out boxes of activated charcoal or baking soda in malodorous rooms. These safe and inexpensive powders absorb impurities in the air, cleaning the odors away and sweetening the room.
The powders can be stored in a discrete place in a cardboard box with holes. After a few days, remove the boxes and discard the exposed powder.
Repeat as necessary to control foul odors.
A solution of half white vinegar and half water is an effective aerosol mist. Use it to absorb odors in the air, by spraying the solution in a stinky room with a standard household sprayer.
In addition to its cleansing properties, vinegar has its own smell that will also mask bad odors.
If Fido brings in the aftereffects of his encounter with the local skunk, use a citrus-based product to remove the offending odor. Skunk spray is oil-based, so the treatment must dissolve the oils; citrus is effective at breaking up oil, and it has its own pleasant aroma.
Mask the Odor
Sometimes, foul odors cannot be removed, but they can be lessened by masking them with another, more powerful scent. Flowers, potpourri, heated oils, scented candles, and cedar shavings are all effective odor-masking strategies.
To avoid having your nose assaulted by one, all-powerful aroma, use a variety of pleasant scents to diffuse the air and cover up the stench.