How does a capacitor work and how do I treat it in a circuit?

for a capacitor the equations you need to know are:  Q=CV  V=Vin*e^(t/RC) and E=1/2QV (with Q=charge/columbs, C= capacitance/Farads, V=voltage/volts, R=resitance/ohms, Vin=initial voltage when discharging/volts, E=energy/joules)

The first equation describes the charge across a capacitor for a given voltage and the second equation describes the voltage, at a given time after the initial voltage, across a capcitor when it is discharging.

The basic function of a cpacitor is to store energy in the form of charge. A capcitor is made up of two plates that can hold electrostatic charge and they are separated by an insulating material. When a capacitor is connected across a battery current will flow and cause elctrons to leave one of the plates and to arrive at the other, hence creating a charge imbalance. This continues until the voltage ( as described by the first equation above ) equals the voltage of the battery.

A diagram of a capacitor and a circuit diagram could be used here to enhance the explanation.