The beginning of the shabbat evening kiddush (vayehi erev, vayehi boker, yom hashishi...) is from Bereshit, 1:31 ff. Where does the second part (khi hu yom tehilah lemikraei kodesh...) come from? Is it also from the Torah?
The first paragraph of kiddush is Biblical verses. The second paragraph is part of the core text of prayers, which were presumably finalized by Anshei Knesset HaGedolah, "The Men of the Great Assembly", i.e. the rabbinic leaders during the early Second Temple period, about 2300 years ago. (See Rambam Berachot 1:5)
The same goes for something like the Amida prayer on shabbat. The paragraphs yismach moshe and elokeinu veilokei avoteinu, retzei vimnuchateinu were composed by the editors of the core siddur 2300 years ago, while it also contains a paragraph of Bible -- "as it says in the Torah ... veshamru bnei yisrael et hashabat ..."
As referenced in the other answer, it's clear that when the Men of Great Assembly composed the core siddur, they often used Biblical paraphrases and references. But it's not "this whole paragraph comes right out of the Bible."
Avudraham cites the following verses for a couple of the lines:
He also gives these non-citation explanations of the sources of the ideas: