Australian Politics

Regarding your edit, no, you don't need a majority of Senators and no party has in a couple decades. What you need to form government is a majority in the House. However, at times when a majority has nog been possible, a PM can be decided when they have a majority of MPs in the House that will vote with them on confidence and supply. Confidence is a literal vote of confidence that happens, where if it fails, the PM is ousted and an election happens. Supply being the budget, which, if it can't be passed, also triggers an election. Hence why Australia could never have a US-style government shutdown.

How do you actually come PM if you don’t have a party that can get a majority vote?

You convince a majority of the members of the House of Reps to agree to support you in passing bills required for operating the government (basically bills allowing them to spend money, also known as supply) and to support you if a motion of no confidence is put forward.

Not senators, Members of Parliament. From the House of Representatives. It's equivalent to Majority Leader in the US House of Representatives, Chancellor in Germany, etc. As long as you can command majority support on matters of confidence, you can become Prime Minister. That's the most important thing the Liberal-National Coalition agreement did for them: the Nationals agreed to provide support for the Liberal leader as Prime Minister. It was similar to the Gillard Government, where Labor didn't have a majority on their own, so they reached an agreement with the Greens and the 4 or 5 independents that they would support Labor on matters of confidence, in exchange for whatever was in their agreement.