What is the proper way to set posts for a long-lasting fence?

Construction Heart redwood is often used for fence posts. The most common dimension is 4x4.

Post depth should be 1/3 the above-ground height plus an additional 6 inches for the rock or gravel bed (Fig. 5). If you experience frost where you live, dig postholes down to a foot below the normal frost line to minimize damage from ground shift due to alternate freezing and thawing of soil.

Post Anchor Alternative.

As an alternative to placing a posts in the ground, concrete footings and metal post anchors may be used, as shown in the example on the left.

See Redwood Fences for All Reason