You can give furniture or you can trade it using the trade window. As others said, the few items of free furniture you got to start with can't be traded or given. I think Stoot said that was to discourage people from creating new alts as a way to get more free furniture.
OK I have made a storage box. I can't take it out of my house, I can't put it in my inventory to give to someone. I am sure this is easy I just don't see it.
There is a furniture slot right beside the Search Bar, and if you click on that you'll see the list of Furniture you own. You can give it to someone if there's a person on your street (but I know you probably know that) or trade with someone.
I wanted to surprise someone by putting a bunch of storage boxes in their house. I crafted them, they were in my inventory, but when I'm at their house, I can't drop them or put them on the wall. Is this by design or am I doing something wrong?