>>2794
>I know it's the flow of electrons and I imagine them being kind of "pushed" from atom to atom.
In a typical conductor, even when not carrying current, some of the electrons are free of any single atom, moving around freely within the bulk material. What happens when a conductor is carrying current is that there is a small bias in the direction the free electrons bounce around within the conductor, so the electrons drift down the conductor.
>I can also imagine maybe a magnet's negative pole (south) pushing away atoms with negative charges, while a positive pole (north) attracts them.
North and south poles don't correspond with positive and negative charges. As a very, very, very rough analogy, if magnetic poles are left-right, electric charges are forward-back.
>I also understand that turbines spin magnets around wires. I don't get why the magnets have to be moving and I don't understand why wires need to be coiled.
Since magnetic poles and electric charges aren't the same thing, then charges are not attracted and repelled by magnetic fields, only electric fields. However, the difference between magnetic and electric fields is a matter of perspective. A field that looks to have no electric part to you will appear to have some electric part to someone or something moving relative to you. It is this electric part that pushes the electrons next to a moving magnet (since all that matters is relative velocity). As for the use of coils, I think that's mostly a matter of efficiency. To get the most out a moving magnet, you want to have a lot of conductor close to it. Also, you want to arrange the wire so that the pushes from the electric fields add together. It turns out coils are the best way to do this.
>I also don't understand how electricity from a generator that flows through a wire will manage to power a machine on the other end of the wire (for example, just making a wheel spin on the other end).
Imagine a long length of wire that's carrying no current. The free electrons are moving within the conductor freely in all directions equally. Suppose, then that someone sets up a positive electric field near one end of the wire. It causes the closest electron to drift towards that end, which creates a place a bit farther out where there are fewer electrons than usual. This cause electrons a bit farther out than that to drift towards that gap, creating a new gap further out, and so on. The movement of this gap is usually much, much faster than the electron's drift velocity.