American witchcraft is what most people on this site are generally familiar with, though it is a more "modern" type of magickal practice. It doesn't have the same long history as some of the other types of witchcraft, and is really just an immigrated mix of other branches of the craft.
Just as the population of the USA is a varied combination, so is the form of magick we would call "American witchcraft". The biggest influence by far has been British Traditional Wicca, begun by Gerald Gardner more than 50 years ago. So much so that many people in America aren't that clear on the differences between Wicca and witchcraft to begin with, but that's another story.
The British form of Wicca and witchcraft came to America in 1962 with Raymond Buckland brought it across the ocean from his own Gardnerian coven studies. He founded his own covens, and wrote several influential books that introduced America to Wicca and witchcraft.
Ok, enough about the history of witchcraft in America, what *is* American witchcraft in terms of what the practice actually means.
Like I said, American witchcraft is heavily influenced by British Wicca to the point where many people don't know the difference. So the majority of people who practice witchcraft follow the 8 Sabbats of the year, cast a circle before performing spells, worship 2 or more Deities (Gods or Goddesses) and often have close ties to nature and the elements.
One unique aspect of American witchcraft is the rise of the solitary practitioner. Original British witchcraft is often performed in groups or covens. America's large Christian and Bible-oriented culture has made it difficult for many witches, Wiccans or Pagans to be open about their practices. And so, that means more people who are going it solo. With the growing number of books on the subject, you can learn quite a lot without a teacher or coven to guide you.
You can also find a wider range of mixed practices, as the multi-cultural population of America influences so many witches. Mixes of Wicca can be found with elements of Santeria, Kemetic (Egyptian faith), Celtic, Norse and many other paths. It's a fascinating melting pot of witchery in America.