The depth of the fence posts into the ground must be at least one foot below the frost level for your region. As well, one third of the total length of the post should be in the ground. This means that in mild regions the posts will be well below frost simply because of their length. In regions with deep frost the posts may have more than one third of their length in the ground.
Gate post and end post holes should be filled with concrete for stability. Intermediate post holes can be packed tightly with dirt. Post holes should be dug with a diameter twice the thickness of the post if it is to be dirt packed, and three times the thickness if it is to be solidified with concrete.
Click on this link to download the Fence and Deck specification sheet Outdoor Wood Project Specifications.