Separate grounding for analog and digital portions of circuitry
Is this to say that the IC's outputs should have a separate ground to
  the IC's power supply (VDD)? If so, how is this possible when all components operate from the same supply?


I suppose your referring to this: 


  Separate grounding for analog and digital portions of circuitry is one
  of the simplest and most-effective methods of noise suppression. One
  or more layers on multilayer PCBs are usually devoted to ground
  planes. A ground plane helps distribute heat and reduces EMI noise
  pickup. Make sure to physically separate digital and analog grounds,
  paying attention to the flow of the ground current.


The current will return back to the source (usually the ground pin of the cable tied to the power supply ground). In the DC world this usually means the shortest path (assuming resistance of the ground plane is equal and the plane is continuous). In the AC world this means the lowest impedance path, which usually means the return current will follow the trace that is carrying the AC signal because of mutual inductance.

Regardless, if a return current crosses through an analog subsection, it will show up as a (usually small) voltage. This voltage offset will cause noise in an analog subsection. 

The best thing (in my experience) is to find where the return current is going and orient the analog subsection so currents do not cross through it. This allows you to maintain a simple grounding system, with a continuous ground plane. 

Another way to do it is with slots in the board:

   

Source: Staying well grounded

A problem with slots is they turn the PCB into a dipole antenna, and if the design needs to be FCC compliant, it may fail. 

Another way is to isolate the grounds with digital isolation, and or a star ground. Both of which I wouldn't recommend.