The short answer to your question is that the Greeks thought of the past as being like their own time, except better.

In his book The Discarded Image: An Introduction to Medieval and Renaissance Literature, C. S. Lewis, though writing about a much later period, draws a detailed portrait of the traditional understanding of history:

All medieval narratives about the past are equally lacking in the sense of period. For us the past is, before all else, a ‘costume play’. From our earliest picture-books we learn the difference in clothes, weapons, furniture and architecture. We cannot remember in our lives any historical knowledge earlier than this. This superficial (and often inaccurate) characterisation of different ages helps far more than we suspect towards our later and subtler discriminations between them. It is difficult to think ourselves back into the minds of men for whom it did not exist. And in the Middle Ages, and long after, it did not. It was known that Adam went naked till he fell. After that, they pictured the whole past in terms of their own age. So indeed did the Elizabethans. So did Milton; he never doubted that ‘capon and white broth’ would have been as familiar to Christ and the disciples as to himself. It is doubtful whether the sense of period is much older than the Waverley novels. It is hardly present in Gibbon... Authors may profess to know that things in Arthur’s day or Hector’s were not quite as in their own time, but the picture they actually paint belies the profession. Chaucer in a flash of astonishing insight acknowledges that in old Troy the language and procedure of courtship may have differed from those of his own day (Troilus, II, 22 sq.). But it is only a flash; momentary. The manners, the fighting, the religious services, the very traffic-regulations of his Trojans, are fourteenth-century.

Just as this understanding survived the Middle Ages by centuries, it also preceded it by centuries more. Consider this mixing bowl, dated to around 470. It depicts the death of Actaeon, an event which precedes the Trojan War by quite some time, but the figures are depressed in contemporary fashions. Contrast especially the clothing of the goddess Artemis in the mixing bowl with that of the goddess in this Minoan fresco.

This is true even in Homer, who in his poems was describing events that were already roughly four hundred years in the past. Bernard Knox, in his introduction to Robert Fagles’s translation of The Iliad notes that the Linear B tablets found by Heinrich Schliemann at Mycenae are “for the most part inventory lists...the day-to-day ledger entries of a bureaucratic monarchy” similar to those in the contemporary Near East but nothing like Homer’s “piratical chieftains,” who more closely resemble the *basileis” of his own time.

The Greeks were for the most part pessimistic about history, believing that as the world moved further and further away from its origins, it grew more and more corrupt and decayed. Hesiod, in lines 106 to 201 of his Works and Days, describes five successive ages of Man: the Golden Age, Silver Age, Bronze Age, Heroic Age (the setting of the major Greek myths), the Iron Age (Hesiod’s own world). There is nothing like the modern idea of progress in this view; humanity’s greatest acts are in the past.

Given that the Greeks had only a limited understanding of periodization and chronology, and that the past was a better, more heroic time than the present, it’s unsurprising that the main use of history for the Greeks was to celebrate the past for the purposes of moral instruction. Herodotus famously begins by declaring that he publishes his history “in the hope of thereby preserving from decay the remembrance of what men have done, and of preventing the great and wonderful actions of the Greeks and the Barbarians from losing their due meed of glory.”

Pre-modern historians tend to report whatever sources they can uncover, inventing freely to patch over contradictions or missing details. They usually cover for this by professing a skepticism about their sources: Plutarch, for example in writing about Thucydides, writes

Let us hope that Fable may, in what shall follow, so submit to the purifying processes of Reason as to take the character of exact history. In any case, however, where it shall be found contumaciously slighting credibility, and refusing to be reduced to any thing like probable fact, we shall beg that we may meet with candid readers, and such as will receive with indulgence the stories of antiquity.

Without modern methods of source criticism, there was little else they could do. Writing a modern history, in which events were situated in their economic, political, and cultural context, was beyond them, as it would continue to be beyond historians until the eighteenth century.

EDIT: Corrected first line.

In between the heroic age and the contemporary world, the picture ancient Greek writers paint follows a gradient from purely legendary material to material that looks more like history:

• purely legendary material of the heroic age -- like mythical genealogies, the Theban Wars, the Trojan War, and the like
• events that were central to how the Greeks conceived of the transition from the heroic age to the present, especially migration legends (the Dorian invasion, the Ionian migration, the Achaean migration, the Aeolian migrations)
• more recent events that supposedly went towards creating the world of the present, like foundation legends (the founding of various early colonies like Cyrene), legends about post-Trojan-War ancestors, and other similar material
• roughly contemporary with the above: several conflicts that are poorly attested and widely disbelieved by modern historians, like the Lelantine War, the First Sacred War, and the first Messenian War
• other events that probably have a historical kernel, but are heavily mythologised -- much of 6th century BCE history would fall into this category, and perhaps also the second Messenian War
• historical events that presumably occurred similarly to how they appear in extant sources.

Everything except the last two categories is generally best treated as purely legendary. There are exceptions. It's possible that the Lelantine War really happened, and Cyrene certainly did get founded. It's just that the details about these stories are not generally tenable.

The ancient Greeks themselves were much more willing to extend their belief to earlier phases. The Trojan War in particular carries a lot of weight, because several chronographers treat the fall of Troy as point zero for their timelines. The most important of the early chronographers, Ephorus, puts it in 1189 or 1149; Timaeus puts it in 1275, 1235, or 1194, depending on which report you read; the Parian marble puts it in 1208; Eratosthenes puts it in 1184; and so on. The next item in the timeline is the Dorian invasion, which happened either 80 or 120 years after that. And so on.

(If you're tempted to take any of these dates seriously, do notice that they also try to assign a calendar date for the fall of Troy -- usually in the month of Thargelion. That is, a month in the classical Athenian calendar. It isn't something preserved in Bronze Age records, it's guesstimation by consensus. For the record, the actual date when pre-Greek Troy was abandoned was around 950 BCE, as determined by archaeological evidence.)

Among sources earlier than Ephorus, Herodotus and Thucydides do treat legendary wars as real, but Thucydides is sceptical about the details. Herodotus does assign dates to some myths, but he doesn't give a systematic chronography: he puts the birth of Dionysus 1100 years before his own time (ca. 1525 BCE), and the fall of Troy 300 years later.

Bear in mind that the Greeks of the classical period knew nearly nothing about the Bronze Age, and nothing at all about Mycenaean culture. They imagined lots of things. But there was no written tradition, and no such thing as archaeology. Some fossilised tidbits from the intervening centuries survived in oral traditions, like the names of a few towns that ceased to exist at some point between 1200 BCE and 700 BCE, but that's not any kind of systematic knowledge -- there's no understanding of how those towns were administered, who lived there, etc. -- and those names don't reach back to the Bronze Age, only to the centuries in between the Bronze Age and the classical period.

Most modern historians do not assign dates for things like the Theban Wars and the Trojan Wars. A few, perhaps, but they're not taken very seriously. The majority of modern accounts will observe that while historical counterparts to the legendary conflicts are possible, there’s no actual evidence in favour of them.

The only positive evidence for legendary conflicts comes from myths dating to the Archaic period. That puts them exactly on a par with evidence for the Sphinx, the Minotaur, and the Hydra: those monsters are all pinned to real geographical locations, like the Theban Wars and the Trojan Wars -- but real locations don't mean the myths are true.