Wicca (sometimes called Wicce, Wicca Craeft, Witchcraft, The Craft, or The Old Religion by its practitioners) is an ancient religion of love for life and nature.
In ancient times, people respected the forces of Nature, by celebrating the seasons and the sun and moon. They saw divinity in the sun, in the moon, in the Earth, and in all life. The creative forces of the universe were personified, for ease of understanding. Feminine and masculine principles of the deity became the Goddess and God (or the Lord and Lady, or any number of various names for Goddess and Gods). These Gods and Goddesses were not superhuman figures. They were embodied in everything from earth, to sky, to people, to plants, to animals. This is still the basis of Wicca. To most Wiccans, nature and all Goddesses and Gods are aspects of Deity.
There are many traditions of Wicca, as well as those who follow a Solitary and/or Ecclectic (picking and choosing from different cultures to find what suits you) Path. There is no such thing as a Satanic Wiccan, because Wiccans do not believe in doing harm to others. All adhere to a code of ethics. We do not do like a lot of modern "cults" and isolate and brainwash impressionable young people. Wiccans welcome new equally respected members... not disciples... or victims.
Wiccan magick is not like the instant "poof" you see in movies or read about in stories, nor is it "power granted to the caster by trapping demons and making them do thy bidding" etc. That's just as it sounds... made up stories and movie magic. Blah. Magick operates in harmony with natural laws. Different spells are used for healing, guidance, or improving lives. The way I like to explain it is it's almost like an answered prayer, although we don't rely on Deity to do the work for us. We work the magick ourselves. Most Wiccans believe in the law of threes... that is, if we do something good for someone, it will come back to us thricefold. The same holds true for evil: if we do something bad to someone, (cast an "evil spell," etc.) it will come back to us thricefold as well. Some simply believe in Karma, without puting a number value on how bad it will come back. Therefore, a witch would never cast a spell to harm someone, unless they wanted something three times worse happen to him or her, or they get hit with a load of Bad Karma.
Some, such as myself, practice alone or with a few others, and some are organized into covens. Some covens are led by a High Priestess or Priest, many by a team of a Priestess and a Priest, and still others rotate or share leadership. Some covens are very structured and formal, with a defined heiarchy, while others may be very informal.
There is no central authority or "Bible" on how to practice, and individual covens vary a great deal. But, most meet on nights of the Full Moon and at eight festivals or Sabbats throughout the year.
Most Wiccans believe in reincarnation and divinity inherent in all human beings and all of Nature. They are always learning, be it from a book or from personal experience. Wiccans keep a personal book, called a "Book of Shadows," where they record magickal spells, rituals, dreams, invocations, songs, etc.
Wiccans do not believe that there is one single path or religion that everyone has to follow in order to reach divinity. That is more for the monotheistic religions. Any and all religions are real, to their practitioners. There can never be one religion that can satisfy everyone in the world. There are just too many cultures, customs, remote areas that have never even heard of the mainstream religions. Not intending to offend anyone, but I just can't believe that a native in some tribe somewhere is going to suffer eternally because they didn't accept something that they never heard of or knew about. They are good, honest, hardworking, caring people. Because of this belief, Wiccan's do not go out and try to recruit new members. If someone was meant to follow this path, they will make the decision and find a way to it.