jtw11:
When talking about separating digital and analog, would one use two separate supplies off the same source - i.e. two 5v voltage regulators, one supplying analog, one supplying digital? Then simply connect the grounds?
You would not normally need to use 2 separate supplies for analog and digital circuitry, although you might use a LC network to filter power to the analog device.
The important thing to realise is that when you want to sense a voltage accurately - such as measuring the output from a thermocouple with the chip you are referring to, or measuring the output from a LM34 or similar temperature sensor by connecting it to the analog input of an Arduino - then unless the measuring chip has a differential input, it is measuring the input voltage with respect to its local ground pin. Some chips, such as the microcontrollers used in Arduinos, even have a separate AGND pin for this. So you need to make sure that the ground side of the thermocouple, temperature sensor etc. is connected as directly to that ground pin as possible. What you do not want is for the ground side of the sensor to share a wire, PCB trace or connector that also supplies power to the chip, or is the return side for a load connected to a digital output - because power or output current will induce a small voltage in the shared ground connection due to its resistance and inductance.
When connecting a sensor to an Arduino analog input, then short of soldering a wire directly to AGND on the IC, the best that can be achieved is to dedicate one of the Arduino ground pins to use as analog ground, and use the other ground pins for power and the return side of outputs. Ideally, they would have designed the Arduino boards with one of the ground pins separately routed direct to AGND.