Duality/Balance
Pagans see a balance in everything. We need hate and love, good and bad, white and black. As an example: without hate we cannot appreciate the beauty of love, and without love we cannot see the ugliness of hate. We need both! Pagans, in general, are good people, but a true Pagan will understand this concept. They are not afraid to hate or to do evil. They are also capable of great love and great good. This is what makes us balanced. Being able to combine the good with the bad is what makes us human and part of nature. We cannot have one without the other. This polarity is what makes the world balanced. Understanding this is a part of what makes a "Pagan."
Nature
Paganism is a nature-based religion. We celebrate the cycles of the sun and the moon. We honor life in all it's forms, and we try to move in harmony with the movement of life, wherever it may take us. All life is sacred and deserves to be respected. However that is understood is up to each individual Pagan. Pagans see themselves as a part of nature, not above it. They must move with it, be one with it. This becomes harder and harder to do in our time and age, but it is possible.
Deity
Every Pagan believes differently when it comes to deity. I personally believe in a God and a Goddess, male and female to provide the needed balance and duality in life. To me, they are simply personifications of life. They are not distant from me, watching the world from afar. They are the world. They are in everything: in me, in the trees, in the wind, in the animals. They are everywhere. They are both equal; one is not above the other, and both are needed to sustain life. The Gods also maintain balance by being both "good" and "bad" at the same time. They are the tornado that rips through the land, yet they are also the sun that makes everything live.
Some Pagans worship Gods from a specific Pantheon, like the Greek Gods, the Egyptian Gods, the Roman, the Celtic, etc. They don't necessarily believe in just one Goddess or one God, nor do they believe they are simply personifications of life. They are real Gods. Many of these Pagans believe and worship the way the ancients did.
Still, other Pagans, myself included, believe that there is still just one God and one Goddess (though not personifications), and these two Gods are known by many different names that can come from the Greeks, the Egyptians, etc. I believe these different names are mere aspects of the one God and the one Goddess. If I am looking for love, I may call upon Aphrodite, the Greek Goddess of love and beauty. But that is just a name for the Goddess. Aphrodite is not a separate Goddess. I'm hoping this make sense! :)
However she is believed, the Goddess is traditionally seen as the Maiden, the Mother, and the Crone. This basically means she knows all, and experiences all, at the same time. In this way, every woman, no matter her age, experience, knowledge, etc., will be able to identify with the Goddess. The moon is the symbol of the Goddess and her three faces can be seen in the changing of the moon as well. The maiden is the waxing moon, the mother is the full moon, and the crone is the waning moon.
However he is believed, the God is traditionally seen as the Horned One. Because he is the Lord of the Hunt, his horns identify him with the beasts of the wild. His symbol is the sun that shines on the Earth and gives life to everything living.
Sacred Space
Pagans do not believe in building temples or churches as places to worship. You cannot call a building made by man a "house of God." Our sactuaries are in the forests, the lakes, the parks, the mountains, everything outdoor basically. The Gods created these and they are in these. To feel closer to the Goddess and the God, all Pagans need to do is step outside and feel the wind on their face and the grass beneath their feet. Better yet, they can even look inside themselves and find the Gods within.
Practice
One difference that separates modern Paganism from the rest of the world, is that it does not advertise or try to convert people. We believe that anyone that is meant for this path will find it on their own. We also believe that ours is not the only path to Enlightenment, it is not the only "One, True Religion." I believe all religions lead to exactly the same place--peace and understanding. There are many paths to this center. What does it matter what path we take, so long as we get there?
In Paganism, there is no need for a bishop or a pope that can be used as a medium to communicate with the Gods. Pagans speak directly to the Gods themselves. There are no followers--only individuals who carry the same beliefs and have the leadersip of themselves. Pagans all participate in ritual, rather than watching a priest do it for them.
Afterlife
Most Pagans believe in reincarnation of some sort. We do not believe you go to one place or another after death depending on whether you were naughty or not in life. One lifetime is not enough to perfect your soul! We believe we are given as many lives as it takes to learn all the lessons we must know. It's my own personal belief that between lives we go to a resting place and review our past lives so that we may choose our next one in order to fix past mistakes or learn new lessons. In life, we still have complete free will, but we gave ourselves a destiny, a fate. Whether or not we actually accomplish it, depends upon the choices we make and the lessons we learn in life.
Karma and the Threefold Law
I can't say whether or not most Pagans believe in Karma and the Threefold Law or not. I can say, however, that I do not believe in either. Karma is the belief that what you do in one life will affect your next life. The Threefold Law, or Law of Three, is the belief that whatever you do will come back at you x 3. But it's all too relative for me to believe. Both beliefs depend on the terms "good" and "bad." While I do believe in right and wrong, I can honestly say I don't really believe in a true "good" and a true "bad." For something to be good, I think everybody would have to agree it was good. Same goes for bad. But that will never happen. Everybody has a different idea of what's good and what's bad. What's considered bad to one person may be considered good to another. It's all relative. There is no absolute. Karma and Threefold depend upon those absolutes. Besides, I also believe that we have to do "bad" things in order to learn from them. Karma and Threefold are supposedly ways to keep practicing witches from doing "bad." But in my own personal opinion, it makes no sense.
Witchcraft and Magick
Everybody knows what witchcraft is, though many have misconceptions. Witches do practice Magick (purposely spelled with a "k" to distinguish it between stage magic and illusions magicians use). Magick is not something supernatural, at all. In fact, magick is actually very natural because it only involves pre-existing energy. Witches learn to manipulate the energy found within and around themselves to make a needed or desired change in the universe. Some witches follow a rule about not using their craft for personal gain, but I feel that's not necessary. Witchcraft originally was used for personal gain. If not used for personal gain, what is the point in using it?
This can be confusing, but not all Pagans are Witches, just as not all Witches are Pagans. Paganism is a religion, a set of beliefs. Witchcraft is the practice of magick. Those are two very different terms, and they are not interchangeable. Also, because it so commonly mislabled, Wicca is not the same thing as Witchcraft. Wicca is a Pagan tradition, much like Catholicism is a denomination of Christianity. Not all Wiccans practice Witchcraft, just as not all Witches are Wiccans.