What happens to electrons in any charging process

That depends a bit on what we are charging. Some examples follow...

Explanation:

If the device being charged is just an ordinary insulator (like a balloon rubbed in your hair), what happens is that electrons from you hair transfer onto the balloon, but only act the point of contact. (This is what it means for a substance to be an insulator - charge applied remains at the location it was placed, without moving.)

If we are talking about charging a capacitor, charge from a battery accumulates on the negative plate of the capacitor and by induction, electrons are repelled from the opposite plate, resulting in a positive charge on that plate.

If it is recharging of a battery, the electrons that are supplied to the cathode of the battery cause a chemical process to occur (called reduction) on the surface of the electrode. This reverses the reaction that occurred during the discharge of the battery, and the battery is then ready to deliver current once again.