From Ground: Use a spade or shovel to dig a wide circle around the hairy sedum plant, aiming for at least several inches away from the plant to prevent from damaging its roots. Start digging deeper once the initial ring is made, and gently lift the plant along with its root ball from the ground once it's sufficiently loose. If the plant is substantial in size, you might want to place it in a wheelbarrow for easy movement.
From Pot: Water the pot thoroughly, then tip it sideways and gently pull the plant by the base. If it doesn't come out easily, try tapping or rotating the pot to loosen the soil and free the plant.
From Seedling Tray: Fill the transplant spot with a little water. Grip the seedling by its leaves, never by its stem, and lift it from the tray. If it resists, use a spoon or a stick to push from the tray's bottom.