The members of the political party which commands a majority in the lower house elects a leader. This leader is then appointed by the Crown as the ‘chief minister’ of the government. At the federal level the chief minister is known as the 'Prime Minister'. At state level, the chief minister is known as a 'Premier'.
Other ministers
The chief minister appoints other members of the governing party as ministers of government and allocates to them individual responsibility for specified departments (portfolios) of government such as health, defence, foreign affairs, the treasury, etc.
The ministers of a government are responsible for delivering the relevant government services and administering the relevant law. In this they are assisted by the public service.