What is the system of how to get our prime minister? We choose our local member who then goes into house of representatives but then what???

The Prime Minister is the key spokesperson of the Australian Government, head of Cabinet, leader of the government.

Role of the Prime Minister in Australia.

Parliamentary Education Office (peo.gov.au)

Role of the Prime Minister in Australia.

The Prime Minister is the key spokesperson of the Australian Government, head of Cabinet, leader of the government.

Parliamentary Education Office (peo.gov.au)

Description

This graphic shows that the Prime Minister is the most senior minister in the Australian Government as well as being key spokesperson for Australia, the head of Cabinet and the leader of the government.

You are right Soph. After a federal election, all the senators and members of the House of Representatives meet with their parties to choose their leader. The leader of the party or coalition of parties with the support of the majority of members elected to the House of Representatives—the government—will become the Prime Minister. The Prime Minister is traditionally a member of the House of Representatives, not a senator.

This also means that, at any time, the government can choose to vote for a new leader who will then become Prime Minister.