Width
The post hole should be roughly three times the width of the post. This width is adequate for both setting the post in concrete and for setting the post in earth. Digging a narrower post hole reduces the effectiveness of a concrete base, and also makes the task of tamping down dirt and setting the post in earth more awkward.
Depth
Post holes should be dug to a depth equaling between 1/3 and 1/2 the length of the post. For a basic post set in the ground, a hole that is 1/3 as deep as the post is long will suffice.
Foundations
Posts set in wet areas may require a foundation, which increases the depth of a hole. In most cases, the post hole should be another 6 inches deep to accommodate the sand or gravel foundation.