It's complicated, but the story is generally written at http://en.wikipedia.org/wiki/Joseph_Franklin_Rutherford.
Some of the problem is that A.H. Macmillan is a major source of information (author of FAITH ON THE MARCH). Macmillan was put on the board of directors by Rutherford, so his story won't be unbiased. Still, the wikipedia story has the legal maneuvering in it.
Trying to weed through the explanation, Rutherford and others were jockeying for positions within the WT corporation before a vote could take place. Russell had intended for a committee to run WT after his death. Russell named Rutherford as one that he considered suitable to be chosen as an initial member of a rotating editorial committee of five elders who were to oversee what material was to appear in the Watchtower magazine following Russell's death. Rutherford managed to get the position of President and then by-laws were rewritten to give the President total charge of the WT's worldwide affairs.
Rutherford said that Russell had such control and that it was more efficient than a committee. The board of directors decided to introduce a resolution to restore the WTS to Russell's intentions and give the power to the committee. But Rutherford had a Philadelphia lawyer's opinion that Pennsylvania law required directors to be elected annually. Some board members had been elected for life- no reelection. Only Rutherford and two others were elected at the last shareholders meeting and Rutherford removed the other directors from office. One officer, Hirsh, had been elected recently, but his election took place in NYC and the law said it should have taken place in Allegheny. After securing a new board of directors (Yes-men including A.H. Macmillan) in Pennsylvania, it was easy work for them to keep power and remove the NY corporation board members.
Basically, a coop took place. The Pennsylvania law of annual reelections was a recent change and was, in the opinion of most, not retroactive and exempted existing corporations. That meant that Rutherford fired directors that should have stayed. Also, the WTS charter said that only directors on the board could be elected as officers and Rutherford was not a director when he was elected President. But what was done was a seizing of power and it could not be undone by ousted members.
WTS has always been a legalistic corporation since then. To be fair, Russell's idea seemed to be that WTS was his baby and no one man would continue with his power. It seemed that he really wanted members to be Russellites, not just Bible Students.