Historically, there were quite a few movements that referred to themselves (or were referred to by others) as Satanism.
At the present, the Church of Satan founded by the late Anton Szandor LaVey calls its tenets Satanism. LaVey even wrote a Satanic Bible.
LaVey's Satanists do not believe in Satan as a personal deity, rather as an archetype.
LaVey has authored nine Satanic Statements:
- Satan represents indulgence, instead of abstinence!
- Satan represents vital existence, instead of spiritual pipe dreams!
- Satan represents undefiled wisdom, instead of hypocritical self-deceit!
- Satan represents kindness to those who deserve it, instead of love wasted on ingrates!
- Satan represents vengeance, instead of turning the other cheek!
- Satan represents responsibility to the responsible, instead of concern for psychic vampires!
- Satan represents man as just another animal, sometimes better, more often worse than those that walk on all fours, who, because of his "divine spiritual and intellectual development, has become the most vicious animal of all!
- Satan represents all of the so-called sins, as they all lead to physical, mental, or emotional gratification!
- Satan is the best friend the church has ever had, as he has kept it in business all these years!
Note: IANAS (I am not a Satanist), I just found this info at http://www.satanism101.com/ .
It has nothing to do with worship, ritual killings, and other Geraldo-invented atrocities.