(א) אִישׁ הָיָה בְאֶרֶץ עוּץ אִיּוֹב שְׁמוֹ וְהָיָה הָאִישׁ הַהוּא תָּם וְיָשָׁר וִירֵא אֱלֹהִים וְסָר מֵרָע.
(1) There was a man in the land of Utz, whose name was Job; and that man was whole-hearted and upright, and feared God, and turned away evil.
(א) פי' בארץ ארם כמה דכתיב את עוץ בכורו מבני נחור
(The land of Utz is) the land of Aram, as it is written: "Utz, his firstborn," in the list of the sons of Nahor (The progenitor of Aram).
This is the basic commentary on Iyov 1:1. However, the idea that Utz is Aram (Syria) comes under attack by the next source:
(21) Rejoice and be glad, O daughter of Edom, That dwellest in the land of Utz: The cup shall pass over unto thee also; Thou shalt be drunken, and shalt make thyself naked.
Whereas Rashi's proof for Utz being Aram is based on the chance that a person's name was transmitted to their homeland, we have concrete, 100% certain, proof that the land of Utz is synonymous with Edom. Tiyuvta d'Rahi, Tiyuvta.
Rashi's opinion, though, is not to be taken for granted. There is a way to reconcile our two beliefs.
Eilat, formally under Aramean governance but actually inhabited by the Edomites, fulfills all the requirements for the land of Utz. So we know that Iyov lived in the Eilat area.
Now on to our second question- When?
Iyov and his friends only use God's four-letter name once in the whole book, and that singular exception may be just an author's revision. The lack of the Tetragrammaton is reminiscent of this following conversation:
(ג) וָאֵרָא אֶל אַבְרָהָם אֶל יִצְחָק וְאֶל יַעֲקֹב בְּאֵל שַׁדָּי וּשְׁמִי יקוק לֹא נוֹדַעְתִּי לָהֶם.
(3) and I appeared unto Abraham, unto Isaac, and unto Jacob, as God Almighty, but by My name Hashem I made not known to them.
God, while talking to Moshe in Egypt, reveals his four-letter name and states that he has previously only used Kel-Shaqqai, the two names excessively used in Iyov for God.
Because Iyov talks about the flood in Noach's days, we can set a starting point for the era in which he could have lived. For the ending point, we put Yetziat Mitzraim, and we get an 800-year period.
(י) אֵ֖לֶּה שְׁמ֣וֹת בְּנֵֽי־עֵשָׂ֑ו אֱלִיפַ֗ז בֶּן־עָדָה֙ אֵ֣שֶׁת עֵשָׂ֔ו רְעוּאֵ֕ל בֶּן־בָּשְׂמַ֖ת אֵ֥שֶׁת עֵשָֽׂו׃
(10) These are the names of Esau’s sons: Eliphaz the son of Adah the wife of Esau, Reuel the son of Basemath the wife of Esau.
(יא) וַיִּשְׁמְעוּ שְׁלֹשֶׁת רֵעֵי אִיּוֹב אֵת כָּל הָרָעָה הַזֹּאת הַבָּאָה עָלָיו וַיָּבֹאוּ אִישׁ מִמְּקֹמוֹ אֱלִיפַז הַתֵּימָנִי וּבִלְדַּד הַשּׁוּחִי וְצוֹפַר הַנַּעֲמָתִי וַיִּוָּעֲדוּ יַחְדָּו לָבוֹא לָנוּד לוֹ וּלְנַחֲמוֹ.
(11) Now when Job’s three friends heard of all this evil that was come upon him, they came every one from his own place, Eliphaz the Temanite, and Bildad the Shuhite, and Zophar the Naamathite; and they made an appointment together to come to bemoan him and to comfort him.
The hebrew adjective "Temani" means "southerner", or "Edomite".
If there are Edomites around in Iyov's day, then we can narrow down the time period to the last 250 years before the Exodus. Also, in Tanach, it normally takes at least few hundred years for names to be re-used (For example: Daniel, David's son and Daniel, the exile; Menashe, the tribe and Menashe, the king; and finally, Yoel, Shmuel's son and Yoel, the prophet). Therefore, we can assume that Eliphaz Ha'Temani is none other than Eliphaz, Esav's son! This gives a time for Iyov: around 1500 BCE.
For a continuation of this discussion on Iyov, see Iyov, Part 2- Elihu and Authorship.