Short answers, pulled from the story.
Classical Greece is conventionally dated from 510 BC, when the last Athenian tyrant fell and Cleisthenes introduced his democratic reforms, to 323 BC, when Alexander the Great died in Babylon. The period covers roughly 200 years, encompassing the 5th and 4th centuries BC.
Cleisthenes reorganized Athens into roughly 130 demes as the basic civic unit, with an assembly of around 10,000 citizens and a council of 500 chosen at random. He divided Athenian territory into thirty trittyes across coastal, urban, and rural zones, assigning one of each to every tribe so that no single economic interest could dominate political decisions. His reforms established isonomia, equal rights for all male citizens, and isegoria, equal freedom of speech.
After the Spartan king Leonidas I delayed Xerxes' army of 300,000 at the Battle of Thermopylae with a force including 300 Spartans, the Athenians evacuated their city and Themistocles commanded the Greek fleet into the narrow straits at Salamis, where the smaller Greek navy neutralized the Persians' numerical advantage and inflicted a decisive defeat. The following year, Greek forces under the Spartan Pausanias destroyed the Persian land army at Plataea. Persia never attempted another invasion of Greece.
The decisive blow came in 405 BC at the Battle of Aegospotami, where the Spartan admiral Lysander destroyed Athens' last fleet after seizing the Hellespont and threatening the city's grain supply. In 404 BC Athens surrendered, losing its city walls, its fleet, and all overseas possessions. Lysander then abolished Athenian democracy and installed the oligarchy known as the Thirty Tyrants.
At Leuctra, the Theban general Epaminondas defeated the Spartan army, killing 400 of Sparta's 2,000 citizen-troops in a single engagement. The battle ended Sparta's long period of military dominance over Greece and the era of Spartan hegemony. It also opened the way for Epaminondas to liberate the helots and reconstitute democratic cities across the Peloponnesus.
Philip II became king of Macedon by 359 BC and expanded into territories held by Athens and other city-states, taking the port of Amphipolis in 357 BC and Pydna a year later. In 338 BC he defeated a coalition of Athens and Thebes at the Battle of Chaeronea. Philip was assassinated in 336 BC and his son Alexander the Great crossed into Asia in 334 BC, eventually conquering the Persian Empire and dying in Babylon in 323 BC, the conventional end date of the Classical period.