When an empty (discharged) capacitor is connected to a battery, it slowly charges up as one plate fills up with electrons, while the other plate has electrons drawn away from it towards the positive terminal of the battery, resulting in one plate having a positive charge and the other having a negative charge.
However, what happens when a capacitor discharges itself? Do I simply assume that the negatively charged plate returns its electrons to the negative terminal of the battery while the positively terminal returns electrons to the positively charged plate, resulting in an end state where both plates of a capacitor are no longer charged (neutral)?
If so, how am I able to power things like an LED with a capacitor, since a LED or any diode only lets electricity flow through it in one direction?
E.g. If I connect a diode to a capacitor (in series), depending on how I place/orient the diode, the capacitor would not be able to charge/discharge?