Charging a Capacitor:

The voltage across the capacitor is not instantaneously 
equal to that of the voltage across the battery when the 
switch is closed. The voltage on the capacitor builds up as 
more and more charges flows onto the capacitor until the 
battery is no longer able to "push" any more charge onto 
the capacitor, at which point the capacitor becomes fully 
charged.
The initial flow of charges from the battery to the 
capacitor means that there is a current flowing through the 
system until the capacitor is charged. This current flow 
decays exponentially from some initial value to zero.
DisCharging a Capacitor:
Switch remains open and voltage across capaciotr decreses 
untill it reaches zero.