In the 5th century BCE, Greece was riding high. In 479 BCE, the combined armies of the Greek peninsula had met the Persian emperor Xerxes' armies at Plataea, killing the general Mardonius and driving the Persians out of Greece in disarray. It was as if WWII Denmark had torn the Nazi Wehrmacht to pieces and scattered it to the four winds - an epic and unexpected victory, and a pivotal turning point in the history of western civilization. The Greeks knew this, and were pleased.
Athens and Sparta had been the two major powers behind the successful defense of the Greek homeland. Sparta, which ruled over a land empire, was satisfied with the outcome of the war and turned their attention to other matters. Athens, on the other hand, was primarily a sea power, and wished to press its advantage and gain ascendancy over the entire Aegean by sweeping it free of the Persian navy. Athens gathered a group of city states into a confederation called the Delian League, and continued to win victories over the Persians all across the Aegean.
Gradually, however, the Delian League became the Athenian Empire. Contributions of ships and soldiers became tributes of gold, taken to a treasury that had been moved from Delos to Athens and were increasingly spent on Athenian building projects instead of the war. Membership in the League ceased to be voluntary. In 470 BCE, the island of Naxos attempted to withdraw from the League; Athens crushed its armies and tore down its walls.
After the war with the Persians officially ended in 449 BCE, tensions between Athens and Sparta rose dramatically. They fought a brief but ugly war in the early 440s, and signed a treaty called The 30 Years Peace, which generally acknowledged Sparta as Greece's dominant land power, and Athens as its dominant sea power. The treaty did little to assuage the hatred between the two powers, however. It also didn't sit too well with Corinth, a Spartan ally which aspired to naval dominance itself. Athens and Corinth fought a series of engagements supposedly on behalf of feuding colonies, which raised tensions further. In 431, another Spartan ally - Thebes - attacked Athens' staunch ally Plataea, and war was declared by all. The Peloponnesian War was on.
Sparta began the war against Athens in the traditional manner. Each summer, as the weather grew too hot for farming, the Spartan armies would enter Attica (the district surrounding the city of Athens) and destroy Athens' crops, killing anyone they could find. However, Athens had constructed a powerful series of defensive walls around itself and the nearby port of Piraeus which the Spartans could not penetrate. So, every summer, the Athenians would withdraw to their citadel and wait out the siege until the campaigning season was over. Then, as the Spartans returned home to tend their own crops, the Athenian armies would sally forth and decimate the lands of Sparta's allies, as they no longer had any crops to busy themselves with. All the while, the Athenian navy brought food into the city and raided the coasts of the Spartan lands. This sparring went on for several years, punctuated by the occasional implosion of one of the combatants' allies, and a terrible plague in Athens.
After Athens' greatest leader, Pericles, died in the plague, the leaders Cleon and Demosthenes assumed leadership of Athens and began pursuing a more aggressive strategy. The fortunes of the two states continued seesawing, but more violently. Athens gained an advantage and snubbed a peace offer by Sparta, only to suffer a series of reverses and the loss of Cleon in 422. Finally, wearied by the incessant (and mainly unproductive) warfare, Athens and Sparta agreed to a peace proposal spearheaded by the Athenian general Nicias in 421.
Much like the earlier treaty, the so-called Peace of Nicias was a failure. The war resumed scarcely a year later. By 418, Sparta had smashed most of Athens' allies, and left the city in dire straits. The rising Athenian leader Alcibiades proposed a daring plan to conquer the Spartan half of Sicily, thus cutting Sparta off from the food and wealth supplied by its colonies on the island. Nicias, ever the reluctant warrior, opposed the plan, but in the end consented in return for command of half the expeditionary force.
A massive armada was assembled. One night, just before its departure, a large number of statues dedicated to Athens' patron god Hermes were "defaced." ("Defaced," because for the most part what the statues actually lost were their erect phalloi, a symbol of fertility.) Alcibiades was blamed, but the navy set sail before anything concrete could be done. Shortly afterwards, however, Nicias' faction convinced the people of Athens to try Alcibiades for the destruction (and other alleged improprieties, which - knowing what we do of Alcibiades - he may very well have been guilty of.) A ship was dispatched; it caught up with the navy and Alcibiades was arrested. However, he managed to escape on the way back to Athens and promptly defected to the Spartan side. He would change sides several more times throughout the course of the war, finally joining the court of the hated Persians.
The invasion proceeded without its greatest general. Initially it was a success, as the Athenians landed and encircled the city of Syracuse, the Spartans' main stronghold on the island. However, the Athenian assault stalled, and despite reinforcements in 413, the expeditionary force was soon backed into a corner. Nicias prepared to withdraw, as the advancing Spartans prepared a blockade to trap his ships in Syracuse's harbor. All was prepared for departure, when Nicias beheld an eclipse: declaring it a bad omen, he postponed the fleet's departure for a day. That night, the Spartans completed their blockade.
The Athenian navy was annihilated. The army attempted to flee inland, but was driven against a river and massacred. Thucydides, in his definitive history of the war, writes that the river literally ran with blood, so great was the slaughter. The 5,000-odd survivors were enslaved and worked to death in Spartan salt mines. Athens' plans were ruined and its military all but destroyed - and what's more, its "allies" began to revolt as Persia entered the war on the Spartan side. Things looked grim.
Nevertheless, Athens rebuilt its navy, recalled Alcibiades, and under his command won a series of stunning victories. In 408 BCE, the Spartans sued for peace - but the Athenians, in a climactic show of hubris, declined. Sparta, drawing upon the nearly limitless resources of Persia, soon constructed an overwhelming navy. Under the command of the Spartan admiral Lysander, this navy swiftly captured the remnants of Athens' once proud war fleet, and in 404 Athens surrendered. Surprisingly, Sparta did not raze the city as was so common in Greek warfare, but it did impose an oligarchic government (The 30 Tyrants) on Athens, as well as tearing down its walls and dismantling its empire. The Peloponnesian war had come to an end.
Ironically, wartime Athens was home to one of the greatest flowerings of artistic and philosophical expression in the history of the human race. It was during the war that the great monuments of the Athenian acroplis - the Erechtheion, propylaea, temple of Athena Nike, and of course the Parthenon - were built, and that some of the most revered art of the ancient world was produced. At the same time, the great playwrights Aristophanes, Sophocles, and Euripides were producing their great classics of western literature. One of Alcibiades' tutors was Socrates himself. It's an interesting comment on the human animal that these people - huddled within their walls, riddled with plague, and facing increasingly poorer prospects for victory - were able to produce such transcendant and enduring beauty, and such wisdom. I find it reassuring that the legacy of such a dark and grim time was, in the end, something greater than misery and death.
This is a very abbreviated overview prepared mostly from memory. I recommend that you check out Thucydides The Peloponnesian War for a more (indeed, almost painfully) complete account. http://www.laconia.org/gen_info_literature/Peloponnesian_war.htm also provides a good, detailed summary suitable for online consumption.