Many old traditions have been handed down and have become more widely known, but most aspects of modern witchcraft are reconstructions as well as simply new practices.
Firstly, the entire field of witchcraft has gotten thoroughly blurred with the religion of Wicca. As I've stated before (and will likely state again), they are not the same thing. Wicca is a spiritual path and witchcraft is a magickal practice. Even so, many aspects of Wicca are now commonly seen in witchcraft even though they are not that ancient or traditional. That's the nature of modern witchcraft today.
That said, the state of witchcraft today is very diverse. How people practice their craft will vary from individual to individual, and this is no longer the mysterious or maligned art that it once was. It's much more accepted and there are more books on the market than you could ever read. It's no longer odd or even a surprise to see people wearing jewelry with pentacles anymore. Larger cities are usually more tolerant of such non-mainstream ideas and you can still find suspicion or distrust in some smaller towns.
You can either be part of a coven, or practice your witchcraft on your own. In fact, there are more solitary practitioners these days than in the past. Materials and supplies are much easier to acquire, and you can shop online or through mail-order to get just about any material you could need.
The bare bones of witchcraft are the same as they've always been. Spells and rituals are performed with an eye to the moon phase, and using herbs and crystals to fine-tune the energy for your intended purpose. Purposes for spells are the same as they have been for hundreds of years: healing, love, prosperity and spiritual enlightenment.
Many witches also perform rituals to honor the holy days of the year, the nights of the full moon or even just the changing of the seasons. It depends on your personal path and lifestyle. Some witches may cast a circle by calling the quarters, but not everyone does. That's one of those Wiccan additions I was talking about.
Basically, modern witchcraft is not too different from historic witchcraft, except that it is getting to be more publicly accepted and understood.