I use a digging bar to make the hole. The post hole digger is to remove the loosened material. I widen the hole at the bottom into a bell shape. Fill the bottom of the hole with gravel and insert the post. I fill the hole with mixed concrete and crown the top so water will run away from the post.
It is important to put gravel in the bottom of the hole so water will drain away from the base of the post. If the base of the post is set in concrete, water will seep down between the post and concrete and never drain; think miniature swimming pool. The post will rot away in a short time.
Some use nails in the bottom of the post to anchor it into the concrete. This will make removal more difficult. I have pulled a post out of a concrete base and driven another down into the same hole before. This is useful if a post splits or badly warps.