The drag item key is the same key (E on PC, X on PS4, A on Xbox One) used for picking up objects. You hold the key until it picks up the item, then you can let go while you're moving around. Press the key again to drop the item.
However, this is also the same key used to exit power armor. Suffice to say, it's somewhat less frustrating if you do your object manipulation while not wearing power armor.
Additionally, you can edit the items in Workshop mode with the same key. Making adjustments in workshop mode seems to subtly alter the object properties, turning the item into static/placed decorations rather than ground clutter.
For example, looted balls placed on a crafted pool table will move around if you walk on the table and bump into them. If you manipulate them in workshop mode, they become attached to the table like crafted decorative objects.