Alcibiades shows up throughout Plato's dialogues, so it is perhaps worthwhile to say something about the charming traitor. The story is about as colorful as it could possibly be, and you can see that from the fact that it starts with a family curse: the Curse of the Alcmaeonids.
In the seventh century BC, a man named Cylon decided he wanted to take over Athens. To do this he consulted the Oracle at Delphi as to what would be a propitious day for a coup. The Oracle replied that he could become a tyrant at the great festival devoted to Zeus. Cylon interpreted that as the Olympic festival. Unfortunately for him, he forgot the first lesson of dealing with an Oracle of the gods: never assume that you know what they mean. His plot failed and his supporters had to seek sanctuary in the temple of Athena Polias. Unfortunately for them, the archon at that time, Megacles of the powerful Alcmaeonid family, simply ordered them all executed, anyway. The Alcmaeonidae were banished from the city for the impiety and regarded as having been cursed by the goddess. Eventually they were allowed back by Solon -- but there was still that hint of being cursed hanging over their heads. Talent seems to have run in the family, so a number of important of people were Alcmaeonids -- indeed, they were major players in the increasing democratization of Athens. One of these great names was Pericles; and, in fact, as tensions began to rise between Athens and Sparta at the beginning of the Second Peloponnesian War, the Spartan embassy (according to Thucydides) told the Athenians to "drive out the curse of the goddess", that is, to remove Pericles from power. Alcibiades was also an Alcmaeonid. And this is perhaps worth remembering because it helps to explain why the people of Athens -- and, indeed, the rest of the Greek world -- were so ready to believe that he was simply capable of anything, and to regard him as a possible danger. There was a miasma, a curse, around the family name. One can see the myths of the Trojan War as a story about how the entire Greek world became tangled up in the Curse of the Atreids; one could well imagine an epic retelling of the Peloponnesian War representing it as a story about how the entire Greek world became tangled up in the Curse of the Alcmaeonids.
Alcibiades was partly raised by his cousin Pericles after the death of his father Cleinias. He was handsome, he was intelligent, and seems to have been an entirely spoiled young man, inclined to be contemptuous of nearly everyone. The notable exception is Socrates, who seems somehow to have gotten through to him. Exactly how their association began is not known, but we do know that Socrates saved Alcibiades' life at the Battle of Potidae, and he may have returned the favor at the Battle of Delium.
Socrates doesn't seem to have been enough. Alcibiades, as he grew older and more influential, began to advocate vehemently for Athens to take more aggressive action against Sparta -- according to Thucydides, this was because he was resentful for having been passed over in treaty negotiations as too young to contribute. Because of this he is said to have sabotaged the treaty, meeting with the Spartan ambassadors in secret and persuading them to rely on his judgment in the negotiations. His ploy succeeded, allowing him to block the negotiators (Nicias and Laches) from actually achieving anything, and resulted in his being appointed General. Never short of ambition, he immediately used his new position to begin building an alliance among Sparta's major opponents -- Athens, Argos, Elis, and Mantinea. The alliance would soon be crushed by the still-mostly-unstoppable Spartan army at the Battle of Mantinea, but Alcibiades kept on scheming.
One of his big projects, after having outmaneuvered some of his political rivals, was the Sicilian Expedition, which was his pet idea. It was vehemently opposed by Nicias, his most influential opponent, but Alcibiades argued that the expedition would contribute to the wealth of Athens and it could be made quite feasible by recruiting allies in the region. Alcibiades had proposed a force of sixty ships; Nicias responded that you would need something like 140 ships. The Athenians decided to do the expedition -- but, in what seems just the first of a never-ending series of disasters, they took Nicias's estimate as their starting point. No doubt they thought they were being cautious and prudent; what they were actually doing was staking a massive portion of their resources on a project whose chance of success they did not know. Alcibiades, Nicias, and a man named Lamachus were put in charge of the expedition.
On the night before the expedition was to set sail, however, someone defaced the statues of the god Hermes throughout Athens. Alcibiades and a number of his friends were accused of the deed. Alcibiades, who may or may not have been guilty, nonetheless recognized that his opponents were taking this as an opportunity to get him out of the way. He demanded an immediate trial, but was denied; he had to set sail without anything being resolved. Alcibiades now out of Athens, his enemies began accusing him of all sorts of things, so when the fleet put into port, it found a swift trireme there that was waiting to take Alcibiades back to Athens to stand trial. Alcibiades managed to convince the messengers that he would follow them in his own ship, but he and his crew used the opportunity to escape. The Athenians convicted him in his absence.
Alcibiades, tacking with the wind, sabotaged the Sicilian Expedition by sending information to the Sicilian city of Syracuse, allowing them to avoid being taken by surprise. The Sicilian Expedition, soon entirely in the hands of Nicias, collapsed miserably because Nicias on his own did not have the range of skills required to organize the whole expedition and fight Syracuse on its home ground and build up the alliances necessary for victory.
Alcibiades in the meantime defected to Sparta, and with his usual golden-tongued oratory somehow managed to persuade them that he should be made a military adviser. But you mustn't get the wrong idea about Alcibiades: anything he set out to do, he intended to succeed at, and so he set out immediately finding ways to destroy Athens. He convinced the Spartans to build a fort at Decelea, because it would cut off the Athenians. This was a devastating strategic move, and far superior to the usual Spartan approach of marching up into Attica every summer.
However, Alcibiades couldn't stay out of trouble in Sparta, either. It began to be clear to a lot of Spartans that Alcibiades was having an affair with the wife of the Spartan king, Agis; and it was commonly believed that Agis's son Leotychides was in reality the son of Alcibiades. What happened at this point is a little unclear, but some say that one of the Spartan generals was ordered to kill him. So Alcibiades defected to Persia, and managed somehow to convince the Persians that he should be consulted on matters related to the Greeks.
The Persians at this point were a sort-of ally of Sparta -- the Persians were technically neutral, and the Spartans certainly didn't trust the Persians, and the Persians were always looking for ways to increase their power in Greek territory, but at the moment they had a shared interest in breaking Athenian domination of the Aegean Sea. Alcibiades seems to have set out guaranteeing that the Persians would not trust the Spartans, doing whatever was in his power to sabotage the alliance. In particular, he insisted that Persia's best route was to avoid committing to helping the Spartans very much -- after all, the more Athens and Sparta wore each other down, the less there would be to stop Persia from swooping in to mop up the remains.
According to Thucydides, Alcibiades was doing this sabotage deliberately in order to be able to argue that the Athenians should let him come back to Athens. This is confirmed by the fact that he started secret negotiations with some Athenians, trying to get them to install an oligarchy, promising that if they did so, he would return to Athens with a Persian fleet and Persian money to fight the Spartans. The war was going increasingly badly for Athens at this point, so a number of Athenian generals were favorable to the plan. The Athenian assembly, after some maneuvering, was persuaded by them to negotiate the matter.
Unfortunately, the problem with being perpetually persuasive is that you are unprepared for when people simply will not be persuaded. And Alcibiades could not persuade the one person who he absolutely needed to persuade in order to make the plan work: the Persian satrap Tissaphernes. Alcibiades had made his previous argument about wearing the Greeks out too well, and the satrap, an intelligent man who had to answer to a higher authority not at all inclined to be merciful to failure, simply refused to commit to anything definite. In a very Alcibides-like move, Alcibiades simply didn't tell his Greek counterparts this, instead coming to them with much stronger demands and giving them the impression that he had convinced the Persians to help, but only if the Athenians conceded much more. It put an end to his plan to return to Athens in triumph -- but he managed to make it seem like it wasn't his fault.
The conspirators nonetheless managed to overthrow the democratic government of Athens and establish an oligarchy. The remains of the Athenian army and navy, considering themselves to be the surviving democracy of Athens -- the Democracy-in-Exile, so to speak -- voted to recall Alcibiades on the recommendation of the general Thrasybulus, probably because they were still under the impression that he really could deliver Persian support. Alcibiades did not dispel the illusion; when he returned to the Athenian fleet, he delivered a famous speech in which he complained about the injustice of his exile and boasted about how influential he was with the Persians. So persuasive was he that the army voted him the rank of general. He was almost too persuasive -- he practically convinced them all to head out for an immediate attack on the Piraeus, so his first act as general was to help Thrasybulus convince them that a more cautious approach would be better.
Then comes what I think is, in some ways, the single most brilliant political move of Alcibiades' career. He arranged to lead a mission to the Persians, promising the Athenians that he would convince the Persians not to send a fleet to help the Spartans. Alcibiades, of course, already knew that nothing whatsoever would make Tissaphernes send a fleet in the first place. In the meantime, one of Alcibiades's longstanding political allies, Critias, managed to convince the oligarchy at Athens to recall Alcibiades -- but Alcibiades was looking for more than just a return to Athens. He wanted to return on his own terms. He remained with the fleet. While he was there, he managed to convince a number of cities to help contribute to the cause, meaning that he was able to pay his men, making him very popular.
In the meantime, things shifted, however. Tissaphernes was replaced by Pharnabazus, and Pharnabazus took a more active role on the Spartan side, actively protecting Spartan sailors when they were driven ashore by the Athenians. Alcibiades led a mission to try to persuade Pharnabazus, but he never got a chance to do it -- Pharnazabus had him arrested as soon as he arrived. He was soon able to escape, but his now obvious lack of influence with the Persians was a serious blow. He managed to maintain his position, however, by some competent tactical work in battle and his still-persuasive negotiating abilities.
Backed by this, Alcibiades decided to return to Athens, where democracy had been restored. He sailed into the Piraeus harbor and received a hero's welcome, but some people couldn't help but notice that he had happened to sail into the harbor on the Plynteria feast, dedicated to Athena Polias. On that day, the statue of Athena underwent cleaning, and therefore symbolically, the city was for that one day not under the protection of the goddess, and anything important begun that day in Athens was doomed to fail.
All charges against him were officially canceled and he was appointed chief general. Misfortune was brewing, however. He set out with troops, and was defeated; his fleet was lost through the error of one of his subordinates; and Cyrus the Younger was made the new satrap by his father the Great King, and he was proceeding with a policy of active support for the Spartans. Moreover, the great Spartan military leader Lysander was too experienced and clever to be outmaneuvered by any tricks or deceptions, and Lysander was winning significant battles. The Athenians repaid military failure in their usual way: they deposed all the generals. The stupidity of this is an example of why Greeks did not generally expect democracies to win against oligarchies in military matters; if your response to failure is to depose all of your most competent and experience people at once, you are likely just accelerating your self-destruction. Which it certainly did here.
Alcibiades never returned to Athens; he sailed north to Thrace and was there for most of the rest of his life. He did attempt to persuade the Persians to stop supporting Sparta, however. According to legend -- and legend is all we have at this point -- Pharnabazus killed him by setting the house he was staying at on fire while he was in it, as a gift to the Spartans. There are other stories; one of the legends is that he helped hasten his death by seducing the daughter of a well placed family.
So now you know something of what Plato and Xenophon and their contemporaries had in mind whenever the name 'Alcibiades' came up.