How does a touchscreen know where your finger is?

The answer

Most modern touchscreens use capacitive technology: the screen is coated with a transparent conductor (usually indium tin oxide) that maintains a uniform electrostatic field. When your finger - which is electrically conductive - touches the surface, it disturbs the field at that point, and sensors at the corners measure the change in capacitance to calculate the exact position. This is why touchscreens don't work with most gloves (non-conductive) and why multi-touch displays can track up to 10 fingers simultaneously by detecting multiple disturbance points.