The Council of the Wise consisted of the Wizards, Galadriel, Elrond, Círdan and others of the chief Eldar. It was formed due to suggestions of Galadriel shortly after the end of the WatchfulPeace. Saruman was chosen as its head, after Galadriel had suggested Gandalf but the latter had refused. The first meeting was held in ThA 2463.
Saruman soon began to betray the Council, because of his desire for the OneRing. At the meeting in 2851 he disagreed with a plan to attack DolGuldur, at the next meeting in 2941 he finally gave in and Sauron was driven (or decided to return voluntarily) to Mordor. At the Council of Elrond, Gandalf says that it was using the devices of Saruman that they were able to drive Sauron from DolGuldur.
The last meeting was held in 2953 to discuss the OneRing, but Saruman lied about the fate of the Ring in order to quieten Gandalf's suspicions about Bilbo's ring and hence gain more time to get hold of it.
According to the "History of Galadriel and Celeborn" in UnfinishedTales?, a Council--described as "the first Council"--was held c. SeA 1700, after the defeat of Sauron's forces in Eriador, at which it was decided "that an Elvish stronghold in the east of Eriador should be maintained at Imladris rather than in Eregion." At this Council Gil-galad made Elrond his vice-regent, and gave him Vilya, the Blue Ring.
The members of this Council probably included many of those who would belong to the Councils of the Third Age, excepting of course the Wizards.