While it would be nice if you could improve the soil before you plant your trees, it is not imperative that you do that unless you have a lot of clay in the soil. To improve it, all you have to do is to replace the soil removed with A good medium such as Pro-Mix DX found in the better hardware stores such as Lowes or Home Depot.

Hybrid poplar trees can be planted much deeper than other trees. You can take a 9 ft. hybrid poplar tree and plant it 8 ft. deep with only one foot of the trunk sticking out of the ground. This tree will grow to have a very strong root system and roots will also grow all along the trunk part that is in contact with the soil. (Planting hybrid poplars trees this deep is standard practice in the Phytoremediation circles where they want to remove disolved minerals from the ground water.)

In order plant that deep, you would need an 8" in diameter auger capable to drill a hole 8 feet deep. While this is not practical for most people, you can still dig a hole 16 inches deep and 10 inches in diameter which is what I suggest.

Ater digging the hole, you could add some loose soil back in the hole, remove the tree from the pot along with the support bamboo cane, and place the root ball in the middle of the hole. Carefully backfill and tamp the soil. Water the tree generously. You can add some fertilizer around the tree but keep it at least 3 inches from the trunk.

Keep the tree watered, first, every couple of days, then every week, for the first year. On subsequent years you can water the trees whenever it has not rained in a week or so, or when there is a drought.