You can drag objects around by holding on them and moving your finger to the place you want the object to go. (You can move it as far as you want.)

You can tap an object to select it, then tap an open space of land, and it will swoop over to that new spot.
(Note that some objects like Chests and Blessing Orbs need a long press to select them, because if you tap them it just activates the object.)