Usually, the higher the capacity of the compressor (the higher the motor horsepower), the larger the compressor tank should be.
The capacity of reservoir tanks is normally measured in U.S. gallons. Here is where you can figure out how to convert from gallons to cubic feet should you have to do so.
Compressors typically operate on a demand basis.
A pressure switch on the downstream side of the compressor tank checks the pressure in the compressor tank, and by extension, the pressure in your plant air lines.
As demand downstream makes the pressure in the air lines drop, so too will the pressure in your compressor air tank drop. When the air pressure in the tank drops far enough it reaches the cut in pressure level, and the pressure switch will send power to the motor to start compressing more air.
When the pressure in the downstream line and the air tank reaches the high pressure cut out set point, the compressor stops.
The difference between the two pressures, and the speed that the air pressure changes between the two set points, dictates how often the compressor fires up.
Having a large tank contributes to less frequent cycling of the compressor, and fewer pressure pulses.
One way industry deals with this is to provide continuous run compressors. When the downstream air pressure drops, these compressors begin compressing air until the high pressure set point is reached. At that point, they stop compressing air, but all the while, whether compressing air or not, the motor still runs.
Depending on the compressor size, and the volume of air required for your application, the receiver may be measured in a few cubic inches to many hundreds of gallons in size.
The receiver size relative to the downstream demand, will allow the compressor to build up a reservoir of compressed air at the desired pressure in the receiver and have it in reserve, so that the air compressor does not have to start every time air is used.
This tank volume will exceed all downstream demand for a period of time. Therefore, once the receiver is filled, your air-driven equipment downstream from the compressor can - perhaps - cycle on and off a number of times without the compressor having to cut in every few seconds to maintain the downstream pressure set point.
It is important then to have a receiver size large enough that the compressor has rest time, not just to help prolong compressor life, but also for additional benefits to having a large receiver, as noted below.
As the air in the receiver cools, it reduces the air capacity for holding moisture, and eventually the temperature in the receiver will reach the dew point of the air, where more water is dropped from the compressed air than would be the case if the air stayed hot. The link is a page explaining more about compressed air dew point.
Less water in the compressed air means fewer problems to deal with downstream as noted on this water problems page. This is information about water problems and how to correct them.
Depending on what the CFM requirements or types of applications I am using compressed air for - I would always have the largest practical air receiver possible for my compressor system.