It is also possible to look at the voltage across the capacitor as well as looking at the charge. After all it is easier to measure the voltage on it using a simple meter. When the capacitor is discharged there is no voltage across it. Similarly, one it is fully charged no current is flowing from the voltage source and therefore it has the same voltage across it as the source.
In an ideal circuit with no stray resistance or inductance, when a voltage is applied to a capacitor, it would instantly charge up and the voltage across it would be the same as that of the source of the electric potential.
In reality there will always be some resistance in the circuit, and therefore the capacitor will be connected to the voltage source through a resistor. This means that it will take a finite time for the capacitor to charge up, and the rise in voltage does not take place instantly.
It is found that the rate at which the voltage rises is much faster at first than after it has been charging for some while. Eventually it reaches a point when it is virtually fully charged and almost no current flows.
In theory the capacitor never becomes fully charged as the curve is asymptotic. However in reality it reaches a point where it can be considered to be fully charged or discharged and no current flows.
Similarly the capacitor will always discharge through a resistance. As the charge on the capacitor falls, so the voltage across the plates is reduced. This means that the current will be reduced, and in turn the rate at which the charge is reduced falls.
This means that the voltage across the capacitor falls in an exponential fashion, gradually approaching zero.
The rate at which the voltage rises or decays is dependent upon the resistance in the circuit. The greater the resistance the smaller the amount of charge which is transferred and the longer it takes for the capacitor to charge or discharge.