Wicca: A contemporary Pagan religion with spiritual roots in Shamanism and the earliest expressions of reverence of nature. Among it's major motifs are: reverence for the Goddess and God; reincarnation; magick; ritual observances of the full moon, astronomical and agricultural phenomena; spheroid temples (Magick Circles), created with personal power, in which rituals occur.
Witch: Anciently, a European practioner of the remnants of pre-Christian folk magick, particularly that relating to herbs, healing, wells, rivers and stones. One who practiced Witchcraft. Later, this term's meaning was deliberately altered to denote demented, dangerous, supernatual beings whp practiced destructive magick and who threatened Christianity. This change was a political, monetary and sexist move on the part of organized religion, not a change in the practices in Witches. This later, erroneous meaning is still accepted by many non-witches. It is also, somewhat surprisingly, used by some members of Wicca to describe themselves.
Witchcraft: The craft of the Witch - magick, especially magick utilizing personal power in conjunction with the energies with stones, herbs, colors and other natural objects. While this may have spiritual overtones, Witchcraft, using this definition, isn't a religion. However, some followers of Wicca use this word to denote their religion.
Another thing is, Wicca is farely new, and new when it comes to being a religion. It was recognized as a religion in the state of Michigan, due to a Court Case. It has since been also recognized by the Army and by several key religious figures. However, it still has a long way to go before it is fully accepted. Witchcraft, is a practice, the practice of magick. A Witch is a "priest or priestess" to the supernatural forces. Yes, supernatural. Some books white-water supernatural as being the SUPER forces that are natural or some crap. Let's face it, if you can bring a lover through a spell, that is pretty supernatural.
So, does the Goddess or God or any other gods fit into Witchcraft? Only if you want it to. Witchcraft is the Craft of the Witch, and each Witch has their own type of Craft. Some Witches might call a favorite god or goddess in a particular spell, or another Witch will rely on themselves to see the spell through. Are both methods wrong? No. However, the one who calls a god has similiar practices to that of a Wiccan's form of magick.
Witchcraft relies on natural objects, personal power and the energy around you to create desired changes. Some Witches learn other things, such as divination (seeing into the future with the aid of a tool, like the tarot or runes). Some go and train their psychic skills (everyone is psychic, you just need to tap inside and see what skills you got and strengthen them). Do you need to be psychic to be a witch, heck no, but does it help? Yeah, at times.
I'm not going to lie to you and say learning Witchcraft (or even Wicca) is easy. It can be fun, hard, depressing, smooth, etc all in one big package. If you stay long enough to open the package and see all the goodies, you might get what you've wanted all along. Whether that is empowerment, love, prosperity, etc.
How do you make Witchcraft work for you? Well, you'll often hear to be positive and that might sound really really DUMB, with a huge capital D. But, they're not kidding when they say that! A spell is a creation from you and the energy you've wielded, and to send negative vibes is like going into the night and tipping a cow. Its not helpful at all. Another good pointer comes from Practical Magic, yea yea, but it is a good strong point:
"You can't practice Witchcraft while keeping your nose down on it."
(Or something to that effect *wink*)