Satanists do not believe in Satan. On the other hand, Satanists do believe in Satan. It depends on what you mean by "believe in" and what you mean by "Satan."
Do I believe in a funny-looking creature in red tights with horns and a tail? No. Neither do I believe in the literalist Christian lie that He is a former angel of Jehovah thrown out of Heaven for being too uppity.
What I believe in is a Satan that represents the so-called "dark side" of humanity. He represents selfishness, anger, lust, hatred, pride and all the allegedly negative emotions. He represents getting whatever you want. He is not "real," in the sense that you and I are real, or the President is real, or the shopkeeper around the corner is real. What He represents is very real, however.
I do not believe in Him the way that Christians believe in their pathetic deity. I do not worship the Dark Lord, nor do I look to Him for a diabolic stamp of approval on the way I live my life. I am the only being whose opinion ultimately matters. I am a Satanist because it pleases me to be so, not because I have been threatened or coerced or deluded into the religion.
Satan is as real as I am. What I mean by this is that insofar as I manifest the Satanic ethos, Satan becomes real through me. I am, at my best (worst?), the incarnation of Satan Himself.
What is the Satanic ethos? At its simplest, it is pure egoism: total and exclusive concern for myself. I am nice to other people on occasion because I want to be, not because someone is telling me that I "should." I could just as easily be cruel to them, with just as much moral foundation -- I was cruel to them because I *wanted* to be cruel to them. More on this idea in a later chapter.
Satan is real because I am real, and we are one. His empire is my empire and it grows daily, giving us greater power and influence. The only "worship" that I do involves pleasing myself by doing whatever I want to do.