The Ostrakismos was one of the new elements inserted into the Athenian Constitution
Every year, during the principal sitting of the 6th Prytaneia, the chairman would raise this question on the agenda: "Should an Ostrakismos be performed?" a vote would take place, and the resolution needed an ordinary majority to pass. If the resolution was passed, a special meeting of the Ecclesia was set during the 7th or 8th Prytaneia.
In this meeting every citizen wrote on a piece of clay the name of a citizen (any citizen) whom he considered dangerous to the polis or to the democracy. The vote itself was anonymous, and strict measures were taken (at least as strict as possible) to avoid multiple voting by single citizens.
Provided there were at least 6000 voters (if there weren't enough voters the Ostrakismos was cancelled), the citizen whose name appeared on the largest number of clay pieces was to go to exile for a period of 10 years. He was given 10 days to settle any unfinished business he might have in the polis and leave Attica. There was no way to appeal. In times of emergency (such as war etc.) the Ecclesia could pardon a citizen that was sent into exile by Ostrakismos. Returning to the polis without being pardoned or before the 10 year period elapsed was punishable by death.
Unlike in other exile punishments (for criminal or other reasons), the name of the person exiled in this way would remain without reproach, and his property was not touched. As the 10 years passed he could return to Athens and could go on participating in public and political life as if nothing happened.
In order to be exiled by Ostrakismos there needed to be no charges, and there was no need even to say against whom the sentence was directed in the Prytaneia sitting in which the decision to perform an Ostrakismos was passed.
Behind the scenes, though, the rivaling groups in Athens were actively recruiting supporters. It is assumed that the purpose in the Ostrakismos law was to prevent potential tyrants, that couldn't be sued for other things, from excercising that potential (one must remember that Kleisthenes created his constitution very shortly after the fall of Hippias, Peisistratus' son).
In later periods the Ostrakismos was used when the struggle between the leaders and factions of the polis brought stagnation in political activity. The removal of the leader of one of these factions allowed the proper managing of the policy that gained majority, but one could never know from advance on whom the verdict would fall.
Response to Gone Jackal
"Ostracism was never bound to a particular crime"
Ostracism was never bound to any crime (particular or otherwise). Period. That is the reason it was always "without mention of charge or reason", there simply wasn't any reason.
The objective of the Ostrakismos was, first, foremost, and solely a political tool (it was certainly NOT just "a convenient side effect"). Take the political significance of the Ostrakismos and you leave it meaningless. It was legislated after the end of the tyranny of the sons of Peisistratus in order to prevent any situation in which any other potential tyrant could realize his potential. It was later used in order to solve problems of political stagnasis and to allow a divided ecclesia to move on in a certain course of action instead of lulling about forever, torn between two, or more, factions.
There is no connection whatsoever and there never has been a connection between Ostrakismos and any other sort of punishment by exile, punishments of exile were abundant in all the ancient (and not so ancient) world throughout history. Most European countries had exile punishments even in the beginning of the 20th century (The US still had it in the 1950's), and they used it quite indiscriminately. They did not have the notion of what you call "pollution". In ancient Greece in certain cases of religious crimes (such as murder and sacrilege), a punishment of exile would be laid upon the convict. That was because otherwise the gods might be angry at the entire city for not punishing the person who has offended them. The punishment in this cases was not only exile (i.e. leaving the country) an integral and inseparable part of the punishment (and according to the opinions of many the most important part of it) was the exile of the convict's family (usually just his immediate family, but we have evidences about cases in which also other relatives were exiled because of their relation to the convict, and without being charged or convicted themselves), the convict's house was destroyed, and all money and property he didn't take with him were confiscated by the polis. He was not allowed to return to the polis until the day he died, sometimes his relative were denied entrance to the city even after his death. If they were allowed to return they'd still not be considered citizens and would not be able to vote or be elected, unless some divine power allowed them to become citizens again. For instance when the archon Megakles of the Alcmeonid family ordered the performance of the execution of Kylon and his supporters for attempting to establish a tyranny in Athens, in the temple of the Erinyes, to which Kylon's allies fled fearing their execution, the entire Alcmeonid house was banished from the polis and even the dead of the family were dug out and thrown outside the borders, as Aristotle says in his Athenian Constitution (Athenaion Politeia):" They were found guilty of the sacrilege, and their bodies were cast out of their graves and their race banished for evermore."* They were only allowed to return to the polis after the intervention of the Oracle at Delphi, and even so they were occasionally thrown out of the polis again for this exact reason. Appeal for such crimes in Athens was done on the shore of Attica, with the convict on a bout a few feet from land, for if he stepped on the soil of Attica he'd be killed. No pardon could be given for such a punishment without divine intervention.
None of the above conditions existed in the Ostrakismos. The exile was laid on one person only. His family didn't have to leave Athens with him. It was for a period of 10 years only. He was given 10 days to conclude his affairs. None of his property was touched. He didn't lose his citizenship. When he returned to the polis he could resume his political career. His name remained pure. And the Ecclesia could revoke the Ostrakismos at any given time (of course this was only done in cases of emergency to the state when the aid of political leaders could be crucial).
On a more personal note: Gone Jackal, this is not the first time we have this discussion, which leads me to wonder, do you even bother to check your facts? I would suggest starting to do so.
*The quote is from the translation found in "The Avalon Project" of the Yale Law School