These opinions are generally based on other references in the text. For example, if I referred in writing to Hessians, you might infer that my piece was set during the time of the American Revolution, whereas a reference to Czechoslovakia would suggest that my piece was set between 1918 and 1992. Of course, this method is neither foolproof nor conclusive, as I could say that Abraham lived in Israel, although the territory was certainly not known by that name at the time.
The most surprising opinion is that Job never actually existed and that the entire story is a parable. This is the opinion of a certain rabbi, and an objection against it is immediately raised by R. Shmuel b. Nachmani, based on the idea that the level of detail in terms of names and places is beyond what would be necessary for a parable. While this position appears to get the last word, no conclusion is reached.
The position that Job was a historical personage is bolstered by the fact that he is mentioned in sefer Yechezkel (the Book of Ezekiel) alongside Noah and Daniel, who were certainly historical figures (see 14:14 and 14:20). While a logical assumption, it is still hardly conclusive. (For example, one might say that someone is "as great as Washington, Lincoln and Superman" or "like Al Capone and Dracula rolled into one," comparing someone with both historical people and fictional characters.) There is also a view, expressed by Resh Lakish, that Job was an actual person but that this story is a work of historical fiction, a la King Arthur or Robin Hood (see Genesis Rabbah 57).
The Talmud starts with the assumption that the Book of Job was authored by Moses, an assumption that makes sense if Job lived in his time or earlier, or if the story is a parable. There is also a debate as to whether Job is a Jew or a non-Jew. The opinions on this also vary based in large part upon assumptions of when Job lived.
For the purpose of these synopses, we will generally assume: (a) that Moses wrote the Book of Job; (b) that it is a parable and that Job is a fictional character; and (c) that for the purposes of the parable, Job is not Jewish. Rather, he is a "righteous non-Jew," who lives according to the seven universal laws commanded of all the descendants of Noah.