Hold the mattock near the end of the handle opposite the head of the tool. Hold the handle so that the pointed pick end of the mattock impacts the hard ground.
Raise the mattock head up and then lower it quickly into the hard soil. Repeat the process so that the pick end of the mattock penetrates and breaks up the hard soil.
Turn the mattock so the flattened end now contacts the ground when the tool is swung down. Use shorter movement with the flat end of the mattock to pull pieces of loosened dirt out of the hole.
Pry out rocks and chop through small roots with the flat end of the mattock. Continue to alternate between the pick and flat end of the mattock to dig a hole large enough for the tree you are planting.