Opamp output to source and to sink
We'll consider this using the ancient (and not very good) 741 op-amp. 



Figure 1. Internals of the ancient 741 opamp. Source: Wikipedia.

From the internal schematic of the 741 op-amp it should be clear that the output can source current from the \$ V_{S+} \$ rail via Q14 or sink current to the \$ V_{S-} \$ rail via Q20. 

In practice this would work as follows:







simulate this circuit &ndash; Schematic created using CircuitLab

Figure 2. Demonstration circuit. RED indicates op-amp output is positive. GREEN indicates op-amp output is negative.

If the op-amp output goes above ground then Q14 will be on and it will source (supply) current out to the LEDs. Since the RED is forward biased it will turn on.

If the op-amp output goes below ground then Q20 will be on and it will sink (consume) current in from the LEDs. Since the GREEN is now forward biased it will turn on.


  The input current of an op-amp is 0 so, how is it able to supply a output current?


The output power doesn't come from the inputs. It comes from the supply rails - pins 7 and 4 on Figure 1. All those internal transistors are used to control the output transistors, Q14 and Q20, and they adjust their conductance (remember that the are made of semiconductor material) to maintain the required output voltage.