Please pick up a book from the table.
refers to any book on a specific table
This sentence below might look as though the article "the" is modifying an adjective, hence it would be acting as an adverb.
I like John. He is the best!!!
Actually the article "the" is not modifying "best". There is an unspoken (implied) noun in this sentence. What is really being said is something like
I like John. He is the best (friend anyone could have)!!!
"The" is still acting as an adjective here. Of course other words could be implied instead of friend depending on context.