If the other side of the capacitor is truly isolated, then you will not get a net charge on the other plate. What will happen is that you will get a charge separation such that the electrons are either pulled toward the plate, exposing a positive charge further away, or they will get pushed away from the plate, exposing a positive charge at the plate. But you will not be able to put much of a charge onto the plate attached to the circuit because a voltage will quickly build up that will prevent further charge accumulation.
If the other side of the capacitor is part of a complete circuit, then a similar thing happens but now the electron that is pushed away can be carried along by the rest of the circuit or the electron that is pulled to the plate can be replaced by an electron coming from the rest of the circuit.
If the other side of the capacitor is part of a complete circuit, then a similar thing happens but now the electron that is pushed away can be carried along by the rest of the circuit or the electron that is pulled to the plate can be replaced by an electron coming from the rest of the circuit.