From Ground: First, water the red flowering gum to dampen the soil. This will make digging easier and can reduce the risk of damaging the roots. Use the shovel or garden spade to dig a wide circle around the red flowering gum, going deep enough to keep the core root system undamaged. Carefully work the spade under the root ball, then gently lift up the red flowering gum from the ground.
From Pot: Water the red flowering gum well and allow the excess water to drain before attempting to remove the red flowering gum. Turn the pot sideways and slide out the red flowering gum gently, keeping the root ball intact as much as possible. If the red flowering gum is tightly root-bound, you may need to tap the sides of the pot a bit to loosen it.
From Seedling Tray: Water the red flowering gum to soften the soil and make it easier to remove. Use a trowel to loosen the soil around the red flowering gum without injuring the roots. Gently scoop it out and prepare it for transplant.