First the name. Sanhedrin is an Aramaic corruption of the Greek word Synédrion, corresponding our word "synod." In Hebrew, it was referred to as the Beit Din or "House of Judgment." The Sanhedrin was the "Supreme Court" of Jerusalem. It had the right of judgment in matters concerning heresy, matters pertaining to the Temple and its courts, and any other authority not assumed by Rome.
The rabbis teach that the Sanhedrin finds its origin in the episode of the seventy elders assembled by Moses (Num 11:16). However, the first historical mention of a governing body of elders in Jerusalem goes back to the reign of Antiochus the Great (223-187 B. C.; Josephus Antiquities,, XII, iii, 3). It likely arose as a governing body of clout with the Hasmoneans after the Maccabaean revolt.
According to Josephus (Jewish Wars, II, xx, 5), the Sanhedrin consisted of seventy members, plus the president. New appointees came to office by receiving the imposition of hands and seem to have sat on the Sanhedrin till death. The High Priest was the president ex officio of the Sanhedrin, as can be discerned from the Gospels. The High Priest was the one who called and summoned the Sanhedrin. (Before the time of Christ, it seems that men other than the High Priest held the presidency.)