It began when the Rebel Aes Sedai traveled to Shadar Logoth and discovered strong residue weaves, stronger than a circle could protect against. Escaralde suggest that the only way to increase a circle past thirteen is to include male channelers. Moria Karentanis then makes an official suggestion to seek out the Black Tower in order to gain use of the Asha'man's aid. 
The sitting was called by Moria Karentanis, Malind Nachenin, and Escaralde with the pretense of questioning a band of sisters who were sent to Shadar Logoth to survey the area where a beacon of saidar had been felt. (Unknown at the time, this beacon was the Cleansing of saidin.)
The five sisters who were sent are the strongest of the Rebel Tower at reading residues. They are Akarrin, Therva Maresis, Reiko, and two others unnamed. Akarrin, the strongest in the One Power amongst the five, leads the group, and testifies that they found a crater that appears to be all that remains of Shadar Logoth. She defers to Reiko, the strongest at reading residues to describe what she observed.
Reiko testifies that she did not recognize the weaves at all, nor could she make sense of them. She suggests that a man or Forsaken could have been channeling saidar to make such an alien weave. Moria asks her if a circle of thirteen could protect against the level of saidar that she could read there, and she testified that they could not.
At this time Escaralde, a brown sitter and one of the three that called the sitting, informs the sitters that the ancient literature indicates that circles can be increased past thirteen if men are incorporated into them and Moria officially proposes that an alliance be drawn with the black tower. The Hall breaks down into shouting after this proposal. Magla Daronos accuses Moria (who actually was a Black Ajah sister) of being a Darkfriend and is about to physically accost her when the Amyrlin Seat calls order using a voice enhancing weave.
After order had returned, the Amyrlin Seat called for Moria to give her opening proposal (speeches are not allowed in the Hall). Moria says that an agreement with the Black Tower will both protect against the Forsaken and their supposed new weapon and also prepare them better for the danger the Black Tower poses. Egwene then calls on those to oppose and in order Magla, Faiselle, Varilin, Saroiya, and Takima speak. These women were the same ones that were surreptitiously sent by the Loyalist Hall to seek reconciliation with the Rebels. Their speeches all focused on the Black Tower and the fact that the Asha'man were destined to go insane by the Dark One's Taint.
After both sides had spoken in turn, the Amyrlin Seat asked those in favor to rise. More than the require amount rose, but the Keeper of the Chronicles, who despite propriety made her opposing views known by crying and shrieking during the debate, called for a greater consensus. Takima openly refused to stand, so the motion was carried through despite lacking a unanimous decision. See the voting history for more specific details. The Amyrlin then asked if any of the remaining sisters would leave their Hall seats as a result of the outcome, but none did.