Satanism has three major offshoots, as best as I can tell.
LaVeyan Satanism is atheistic humanism with ritual magic. It is the worship of the body and physical pleasures. It was first espoused by Anton LaVey, the Black Pope of the Church of Satan, during the 1960's. Their headquarters is in California. To be a card-carrying member, you pay a $200 dollar membership fee that allows you to attend their meetings, which are, again, of virtually zero use to you unless you live on the West Coast.
Theistic Satanism is what most people think of when they think "Devil worship." It is the worship of Satan as he has manifested through the lens of the Bible and thousands of years of Christian interpretation. (The latter half of that sentence is a necessary disclaimer; Satan and his domain - Hell - appear conspicuously few times in the Bible, so most of what we understand of him is the product of opinion and interpretation gleaned through literature like Dante Alighieri's Inferno.) There's not many of these around.
Finally, there's Luciferianism and other like sects. These worship Lucifer as a beacon of truth and light. Sometimes he's an archangel from the Bible; other times, he is interpreted through the Sumerian pantheon, where he assists mortals against the wicked will of their creator Gods.
As a practitioner of a sort of LaVeyan Satanism, I can tell you the major appeal is for self-worship; the deification of the magic practitioner and his or her initiates. Satanists don't beseech the Gods for assistance; they command it. Its rituals and rites have a more macabre, domineering tenor than those in Wicca, which I believe to be a better reflection of humanity's relationship to the elements - and the universe as a whole - than the rosier picture right-hand pathists paint.
Hope this helps! Blessed be.