Imagine putting two positive charges near each other. Each creates an electric field pointing away from itself. The other charge sits inside that field and is pushed away.
Now replace one with a negative charge. The negative charge responds in the opposite direction, so the two are pushed toward each other.
That's it.
The interesting part is that the charge doesn't need to touch the other charge. It responds to the field that exists at its location.
That's the Faraday's great conceptual shift:
