first are you required to file for a building permit? if so, pier construction is not prescriptive code in most areas that use the International Residential Code. Put a call into your local building department to find out.
with that said your footing must be able to support the weight of the construction it supports (dead load - weight of building materials) together with all other imposed loads such live load (people, furniture, snow, non-permanent loads). The size of the footing is based upon the total load and the soil bearing capacity of your soil.
footings must be supported upon undisturbed virgin soil with a depth at least meeting your frost depth (ask building department for yours). You may need to go deeper depending on the type of soil at your frost depth.
Pier may be either square or round (sonotube type) and typically are reinforced with steel reinforcing bars to resist any lateral loads.