In English there is difference between movement and state.
I go down.
I am downstairs.
This difference doesn't exist in Italian.
Vado giù. => I go down. (adverb)
Lo mettogiù. => I put it underneath. (pronominal adverb)
Lui è già giù. => He is already downstairs. (adverb)
In English the situation is complicated. Down is an adverb, but is used together with a movement, underneath is a pronominal adverb, describes the position in relation to something else, and downstairs is an adverb as well, but is used to describe a static relationship. The english system is complicated, the italian system very easy: giù, giù, giù.
But both languages distinguish between the adverb and the preposition.
Lo ha buttato giù. => He threw it down.
Lo ha messo sotto il libro. => He put it under the book.