You will find that on the left-hand path (defined - depending on the perspective of the individual defining it - as followers of other than christ from a christian perspective, or as those working the "dark arts" or "black magick" from a more Wiccan perspective) that there are many different theologies. Many practitioners are truly eclectic practitioners - meaning that they borrow from any number of practices. However, the most "traditional" form of Satanism is LaVeyan Satanism (founded in 1966 by Anton LaVey). You can learn more about it at http://www.churchofsatan.com/Pages/index.html and http://en.wikipedia.org/wiki/LaVeyan_Satanism.
There are a number of differences between our order and that of Anton LaVey.
In LaVeyan Satanism, the individual practitioner is considered to be their own god. Our beliefs are close there, in that we believe that all of us are inherently already gods and goddesses. However, the LaVeyan theology also teaches that there is no afterlife - the idea that this life is all that there is. We know that there is an afterlife - that we do go on.
One of our goals is to free ourselves from the dominion and authority of god. Once we free ourselves from the dominion and authority of god while in this life, then we are not subject to his judgment or restrictions. Instead, we will walk past god and his christ, and take our rightful places as the Gods and Goddesses that we truly are - at least equal to if not far greater than god and his christ, and all of those poor souls that will be trapped endlessly singing praises to them as their slaves.
LaVeyan Satanism teaches that Satan (or Lucifer) is not a being or person. We believe that Lucifer is a person as described here.
Like LaVeyan Satanists, we believe that taking power, strength, and pleasure for ourselves in this life is essential. We must be able to learn from and appreciate them in order to accept our godhood. We also believe that doing so serves to weaken god.
Like LaVeyan Satanists, we do not believe in sacrifices or offerings to Satan - including children or animals. We too do not fast.
Unlike LaVeyan Satanists, we do not use a nude woman as an altar in any ceremony. We do believe that rituals may be practiced sky-clad according to the desires and comfort of all participants.
We see ritual as more than cathartic. Ritual is designed to help focus the mind and will of the participants upon the desired outcome, as is all of magick.
Most traditional Satanists keep images of death - such as a skull - on their altars. We believe that the configuration of your altar is a personal thing, but there is no requirement for skulls or other images of death.
LaVeyan Satanists practice based on 9 Satanic Statements and 11 Satanic Rules. There is some truth in them, and some things that are not a part of the beliefs and practice in our order. We do generally believe in indulgence versus abstinence, the inherent right to self defense, and some of the other items in their practice.
To read more about our specific beliefs, click here.
So mote it be.
High Priest and Magus
The Liberated Of Lucifer