ANSWER - Well it's one out of ten for effective use of Google from me... There are witchy pages all over the internet covering this. Though if I'm honest I can take your point, many forums and pages do assume the basics and what you're asking about here are the real fundamentals.
In a nutshell Witchcraft is about the manipulation of intent and energy. It is about infusing the creativity of desire into the actuality of tangible outcome. Witches as you rightly remark do use tools to achieve this manipulation and both the wand and the athame (knife) that you comment on are used to direct energy within magical workings. Witches use other tools as well, tools less flamboyant than the ritual knife. Oils, crystals and herbs are all likely to play a part in the path of the average working witch.
As for what we actually do, well practise of magic varies wildly between individuals. Magic can be as simple as stirring a little well wishing into the evening meal (the transferring of intent to deed, in this case the altered state of the diners) or it can be as complex as raising energy to create a sacred space and conducting a formally written ritual with the use of specific wording and symbolism (and no, before you ask, not necessarily performed naked...)
There is no one answer to what we do because we all do different things. Some witches will only perform magic in a circle, others never use a circle, some use tools, others don't. The individual's practise is honed over time with the experience of what does and what doesn't work. Eventually a practised witch adopts tried and trusted methods of working and these grow to form the basis of her ever developing relationship with magic.