Simple Solution:
As the trappings of the "new age" enter the mainstream, we see smudge
sticks in stores, and read recommendations here and there for "space clearing" and purification, using smudging techniques and burning incense.

Smudging is used and recommended by indigenous peoples, feng shui
practitioners, healers, and more. A Native American healer I respect smudges his computer every night. What is smudging? Why do it? Why learn about it?

Here is what I think smudging is, and why it is often a very useful tool
to use in the home.

Healers often recommend smudging to change the "energy" of a place after
an event has happened, such a death, or even an argument. Smudging a computer would be done to remove the electromagnetic field energy; smudging one's desk at the end of the day could be to remove the "work" mentality from the air; smudging after an argument would be done to clear the air, quite literally.

I think that smudging works to change the energetic of a space because of
the science of entrainment. Our senses respond to vibrations, and there is a law of physics that makes vibrations want to start being harmonious, to be in synchrony. Entrainment is a word often used with music. In sound healing, the dissonant chord is gradually influenced by the harmonious cord and the
disharmony changes to harmony over time.

Even air has a vibration, held I believe in the humidity. The water of the
humidity would absorb the negative "vibe" of an argument, for example, and hold it. If you burn a healing plant, such as sage, in such an atmosphere, the humidity would then hold the energetic of the healing plant, and bit by bit the discordant energetic of the argument would be influenced by the harmonious vibration of the plant smoke.

The herbs burned are usually sage (white in particular), sweetgrass, or
cedar, although any dried herb is fine, even lavender. If the herb has too woody a stem, the leaf part will burn very fast and die out.

White sage is a good choice because the leaf clusters are very long, and
the leaves will smolder for quite a long time, emitting smoke into the air. Sage is also known as a purifying herb. Sweetgrass burns very quickly, and is a great choice for emanating sweet smell into the air (and healers believe sweet grass brings a high level of spirituality and burns away negativity). Cedar is very strong, and is considered powerful for removing negativity.

Buy your smudge sticks from those who honor the plants and bundle the
herbs with sacred ceremony of appreciation. If you grow your own herbs, research making smudge sticks and honoring the plants.

To burn herbs, and create smoke, you have to be very careful not to start
a fire. I use a big ashtray, with steep sides. Some light whole bundles of
herbs, but I don't because there is no need, usually, for that much smoke.
Instead, I untie a smudge bundle and pull out just a few leaves, and light them. Once there is a flame, you blow out the flame (making sure you catch any sparks in the ashtray). The herbs will smolder, and the smoke will waft into the home. Walk around with the ashtray (smoking herbs included), and make sure the smoke reaches into all the areas of a room you want.

When you are done, let the herbs extinguish on their own (if they are
safely in the ashtray and away from wind), or extinguish them fully with water.

As I think about smudging, sitting here on the cusp of spring and winter,
I can see how smudging out the winter mood's to let in the renewal of spring is a great use of smudging.