Things are connected to other things by little conductive “wires” called traces running through these different layers, which lets traces cross without shorting. If you look up an image of a single layer PCB, all the traces are visible and don’t cross each other.
If you’re asking about how electricity can be directed to different places without moving parts, that would be the magic of the solid state transistor, and the logic gates that can be constructed out of different configurations of transistors.
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