The Elements
Not all witches use elemental correspondences, and among those who do, there is a great deal of variation. The most common elements used in Wicca and Witchcraft are earth, air, fire and water. Spirit is often added to acknowledge the spiritual component of them all.
When invoking the elements, they are often associated with the cardinal points. Often air is in the east, fire in the south, water in the West and Earth in the North. This isn't the only possibility though. The elements may also vary as well.(ex: some Celtic traditions use earth, sky, and water, and others use the cosmological realms of the underworld, earth and sky)
These correspondences are some possibilities among many. My sources for the following information include: Eileen Holland, Scott Cunningham, Silver Ravenwolf, Amber Wolf and Yasmine Galenorn.
When casting a magick circle, something to represent each of these elements should be present in the circle when the spell is cast. ex: Salt for earth, incense for air, candles for fire and water for, well, water. :)
Elementals:
Elementals are fascinating things. They are both powerful as well as dangerous at times. If you've ever spaced out on a candle burning or stood on top of a cliff-only thinking it would be a rush to jump off-you have witnessed their power. Elementals are said to reside in the Faery Realm and are also called devas or djinn. You can contact elementals through invocation. They can be found in places where you would expect them to be: ex. a beach, a brushfire, a windy canyon, etc.
Some people prefer certain elements compared to others. It can usually have something to do with your astrological sign (ex: fire sign, such as Aries, Leo or Sagittarius with fire element.)
It is said that elementals are dangerous to work with (except earth), primarily because like spirits, they are easier to summon than to banish. I have never worked with them myself, but have heard of people having bad experiences working with them. A friend of mine decided to invoke a fire elemental, and a week later, her son's apartment building burnt to the ground. It might just be coincidence, but I'm not sure if I want to take that chance.