"It is written in the book."
Translation:Det står i bogen.
Det skriver i bogen means "It writes in the book". at stå (or staa if you don't have the å key) is used when something is written on a page (e.g. in a book or newspaper)
Edit This is also as well as to literally stand on two legs or something standing on something else (e.g. Det står på bordet = It's on the table)
Think of the letters as little guys standing in line waiting to be read ;-)
"It is written in the book" = "Det er skrevet i bogen", "Det står skrevet i bogen", "Det står der skrevet i bogen". "It says so in the book", "The book says so", "So says the book" = "Det fremgår af bogen", "Det står der i bogen", "Det står i bogen", "Det siger bogen".
Maybe I am starting to over think it.
In most Germanic languages, inanimate objects either lie, sit or stand. English is unusual in using the verb "to be". Writing refers to the act of creating the letters, but once they are created, they exist on the page without the act of writing any more and because when we read them, we view them with an aspect of verticality, they are said to "stand" on the page rather than "sit" or "lie". English is actually unusual by using the passive voice and the creative action (writing) to describe the location of letters and words.