Luciferian witchcraft is one aspect of the black magick path, and though it's not as common as others, I have seen many people here looking for more information, so here it is.
Firstly, there can be some confusion about the being known as Lucifer. In some spiritual circles, Lucifer is known as the "light-bringer" and is the God paired with the Goddess Diana. This is typically an Italian or Stregherian approach, and these two figures were the parents of Aradia, the Goddess of witches.
But more often, Lucifer is seen as another name for the Christian devil or Satan. That's the viewpoint we're taking here. The general approach is that Lucifer was once an angel who fell from heaven (as told in Biblical history), but that doesn't necessarily make him the fully evil figure of Christian myth. He is better connected to mankind, and embraces both the light and dark sides of magickal energy.
So Luciferian witchcraft tends to be a blend of ceremonial magick that uses a lot of sigils (magickal symbols), talismans and various forms of sex magick. It's not really the same as Satanism or "devil-worship" but is a true form of witchcraft that goes beyond the belief in a Satanic figure.
There are several books on Luciferian witchcraft, and I suggest that you get a copy of one of them to research this further. It's a less-mainstream form of witchcraft and not one that I can simply explain in just a few paragraphs (particularly since I am not a follower of this particular path myself). Some of the better books on Luciferian witchcraft include: