Do not press too firmly, only enough to hold the tree upright. This method of backfilling with soil and water will remove large air pockets. Construct a small dam three feet in diameter around the tree. This dam will help hold water until it percolates into the soil. Mulch is simply organic matter applied to the area at the base of the tree.
Some good choices are leaf litter, pine straw, shredded bark and twigs, peat moss and wood chips.
Mulch will hold water for the tree, reduce the amount of grass and weeds around the tree, provide a slow source of nutrients and organic materials, and moderate root zone temperature. Maintain this area by adding mulch as needed for approximately two years. Do not allow other vegetation into this mulched area, as it will compete for water, nutrients and air that the tree roots need. If the tree will stand alone, staking is not recommended. Periodically check wires for proper looseness, and remove all wire and stakes, if possible, after one year.