What exactly does a capacitive touch screen need to register input, and how can that signal be produced?

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There are active styli out there, and they take 3A or 4A batteries and don't require any wireless connection. How do those emulate human touch?

EDIT: I am specifically interested in iPad touch screens. After some research, I have realized that there are many types of capacitive sensor tech, but most people seem to be in agreement that Apple uses mutual capacitive projected capacitance sensor arrays. These are set up with a grid of capacitors. A voltage is applied to one axis, and the other axis reports change in voltage when the local electric field of a finger alters mutual capacitance of the capacitors directly underneath it.

EDIT 2: what I really want is something with a fine tip like a ballpoint pen to project about a 5mm electric field the same way that a human finger does. There are styli on the market that try to work with a fine tip, but they all fail and I do not want one. I want to make my own because DIY projects are way more fun than buying an overpriced failure of a product.