There are different types of capacitor and of course the type of plate and dielectric makes it different from each other. Since the essense of the capacitor is to charge and discharged electric current. It can be charged by energising itit, definitely by connecting it to a power source with each terminal both positive and negative well connected to power supply source. Of course it must be a DC power supply source since capacitor is a passive electronic component. It can only be fed with a DC voltage.
Provided the voltage is not too high or arbitrary for the capacitor, with time there will be a build up voltage in the capacitor and it will charge up with time. Though, the charging depends on the type of capacitor and voltage in.
Also to discharge a capacitor, you will have to connect the capacitor in parallel with a resistor of higher killo ohms which is expected to drain off all the voltage voltage with time.