Determining how deep your posts should be set is a very major decision as it is the basis of how sturdy your fence line will remain through wear, tear and freezing temperatures.
Here is a simple way to determine how much digging you need to do to secure your fence posts.
Your main concern is freezing temperatures. Below is an Air-freezing Index that can help you determine the index for your area.
Based on your air-freezing index, use the table below to determine the depth required to pass the freezing line.
If you are having a fence contractor install for you, make sure to ask them the length of the posts they are installing. It will need to be equivalent to the height of your fence PLUS the Footing Depth required for your area according to the above chart.