How do wires work/get manipulated?

Wires just carry electrical signals, they have no brains of their own. But at the ends of the wires we have devices that control the amount of electricity being sent through the wire, and at the other ends there are devices that respond to that electricity.

One of the simplest arrangements is a telegraph, in which the button you press completes a circuit that allows electricity to flow. The electricity energizes a magnet that pulls on a clicker. Using pre-arranged patterns of clicking (Morse Code) allows the operators to send messages to each other.

Then there's the telephone. Instead of a clicker, a microphone's diaphraghm picks up the vibrations of sound waves, and pushes on a coil-and-magnet arrangement, which creates a small amount of electricity directly related to the amount of sound it received. That electricity goes down the wire to the other end, where a speaker built much like the microphone turns varying amounts of electricity back into sound waves.

Your mouse is much more complex, but still works on the same principles. A sensor detects when the mouse is moving (older mice used balls and rollers, newer ones take laser pictures of your desk) and a chip translates those movements into a series of codes to be sent down the wire. On the other end, your computer interprets the codes and uses them to decide where to draw the mouse pointer next.

The wires don't do anything special, they're just long strands of metal with a plastic coating.

It's the electronics at either end of the wire that control what happens.

In a mouse, a small micro-controller drives sensors that detect changes in reflected light from the surface it's on. This data is encoded as short pulses of electrical current that travel through the wire to the computer. The computer interprets the electrical pulses and uses them to move a cursor onscreen.

All computer cables are made from copper. Copper allows electricity to pass through it. When you use a mouse, electric signals pass through it. Meaning that the voltage of the electricity will vary. The computer picks up these variations in electricity and translates them to signals which are then translated into commands that tell the computer the mouse it moving up or down or the button has been clicked.