Just in case you were wondering, the Archbishop of Sydney is not the chief clergyman of the Anglican Church of Australia. That is Dr Phillip Aspinall, Archbishop of Brisbane. Also, methods of appointing bishops differ very much within the Anglican church. Typically they are elected by a synod. In the Church of England they are nominally appointed by the monarch, although the monarch acts only on the advice of the church.
The new Archbishop of Sydney will be elected by a special "election synod" (a parliament of representitives of the church, generally both clergy and laity) over the 5th-9th August.
The election of the Anglican Archbishop of Sydney is a robust, competitive and energetic internal church process, where candidates' personal lives, doctrinal views and pastoral actions are scrutinised closely, openly assessed and lobbied over. The election synod can be both unsettling and tense for Sydney Anglicans as they seek to identify the successful candidate.
I don't know what the minimum qualifications are, although I assume you would have to be a member of the Church of Australia. You do not have to already be a bishop, and there have been recent appointments of non-bishops.