No separate power supply is required. You put your control signal on the input and your load on the output. The other side of the load will be connected to a positive supply.
This would be a typical connection. The "common diode" connection (pin 10) isn't required if your loads are resistive, but if you are driving relays or other inductive loads then you would connect it to the positive supply to clamp spikes when the load is turned off.
The IC is an integration of an array of darligton transistors at each channel. Pin 1 of the IC is equivalent to the base of an NPN transistor and PIN 16 is the collector of the same transistor whose emitter is grounded. A free wheeling diode is internally connected from every output pin to a common pin 10 in your case. Below given is the internal circuit of each channel inside the IC. Refreing the datasheet will guide you better with more details and specification with schematics.