Christian witchcraft can be a very contentious topic, and will almost always bring out arguments in people. Not quite as bad as Christian Wicca (something altogether different and possibly another page is coming on that), but it's a rough thing to discuss.
Christian Wicca attempts to combine two religious paths, but Christian witchcraft is a religious approach to a non-religious practice. Witchcraft itself isn't a religion or really attached to any religion, so it can be used along with any faith just fine. The general idea is to perform witchcraft spells and rituals, but invoking the spiritual presence of God, Jesus and sometimes the Holy Spirit or the Virgin Mary.
The big issue that most people have with Christian witchcraft is that witchcraft is rather specifically forbidden in the Bible, and therefore you are breaking the rules trying to mix the two. I mean the Christian rules. Witchcraft itself doesn't really impose rules about itself. Anyway, the big verse is:
Exodus 22:18 Thou shalt not suffer a witch to live
Now, many people have since proven that the translation on this is poor, and that the word "witch" really should read "poisoner", leaving witchcraft out altogether. Then again, there is:
Deuteronomy 18:10-11 Let no one be found among you who practices divination, sorcery, interprets omens, engages in witchcraft, or who is a medium or spiritualist.
That's actually pretty clear, and there are other verses scattered through the book that echo the same ideas.
Well, there are also verses in the Bible that forbid the eating of seafood or clothing made with mixed fibers. Most people tend to ignore those, so why not the verses about witchcraft too? My point is that's it really isn't that simple to judge. So keep an open mind about Christian witchcraft and don't assume that it's a contradiction in terms.
Now that we're clear on the "contradiction" between Christianity and witchcraft, what exactly does this sort of practice look like? Unlike the other types of witchcraft that are based on certain cultures, Christian witchcraft is not.
That means there are no historical spells or rituals to use. It's generally a Wicca-like set of spells (like the ones you find all through this site), but more often there is a Deity component added to include God or Jesus. Basically a standard spell with a prayer added on.