There are various kinds of Satanists that each describe Satanism in their own unique ways and have squabbled over the real meaning.
Satanism is not one belief system like a religion. Satanism is a wide range of beliefs and theologies that have a positive view of the figure of the figure we call Satan.
The most common "school" of modern Satanism is regarded as "aethetic" Satanism: they see Satan as a symbolic figure of ambition, non-conformity and the power of the will. A symbolism more than an actual person or deity.
The best-known symbolic Satanist organization is the Church of Satan, founded by Anton LaVey.
But there are a growing number of people who worship Satan as a deity.
Generally, these people don't regard Satan as the figure known in Christianity, but revere him as the image of an Ancient God descended from ancient polytheism - a modern-era version of:
Egyptian god Set,
Greek Titan Prometheus
Sumerian god Enki.
I believe that the Temple of Set is the largest organization that subscribes to such a belief.