Capacitors do not work alone (and shouldn't work alone). In fact, a capacitor typically works alongside a resistor. Why? Because mathematically, the capacitor recharge and discharge depends on the resistor (we'll get into the theory of that later). The value of the resistance can alter the time it takes for the capacitor to recharge and discharge (releasing the current).
A pair of resistors and capacitors, whether working in parallel or series, can produce different behaviours which we can use to, for example, switch LEDs ON and OFF for a certain duration and low-pass or high-pass filters for radios.
Let's see how a capacitor actually works.
The simple circuit above will demonstrate how a capacitor charges and discharges and how it can still light an LED even without the battery being connected to the circuit.