Decoupling Capacitors: What happens to the DC on the cap once noise is introduced and it shorts?
The capacitor does not "short out", it has charged up to a constant voltage by storing energy as electrical charge, and if something external tries to change the voltage over the capacitor, it means that more or less charge is needed to change the capacitor voltage up or down, and moving charges means is current flowing.  

So in short, a capacitor wants to keep the voltage over it constant, and resists any voltage changes by combating it with current. So voltage spikes get attenuated because the capacitor uses energy of the spike to change charge, and the larger the capacitance is, the less the spike can change the capacitor voltage.