The Australian Senate is similar to the US Senate in that each original state has an equal number of Senators. As there are only six states each was given six senators when the Commonwealth came into existence on 1st January, 1901.

The Australian constitution has what is called a nexus provision, so that the House of Representatives (apportioned by population subject to each state having at least five members) is required to have approximately twice the number of members of the Senate.  

Australian politicians hate the nexus provision, because it means that every time they want to expand the size of the House, they have to put up with more senators. Four constitutional amendments to break the nexus have been put to the Australian people in referendum and each time the proposal has been defeated. The current position is that each state has twelve senators.

It seems the original idea of the Senate was that it would represent the states as such. However it actually functioned as another house where party interest was more important than state interest.

The normal position is that half the Senate is elected every three years, to serve a fixed six year year term commencing on the 1st July next after the half Senate election. Since 1948 the Senate has been elected by the single transferable vote method of proportional representation. This can present difficulties to the voter as they might have to rank 60 candidates or more, due to the Australian federal requirement that a preference be given to every candidate to make the ballot valid (formal in Australian terminology). However the option is given of voting "above the line", which enables the voter to accept the preference schedule of the party of his or her choice rather than having to construct one of their own "below the line".

With STV a party must get a seat if one of its candidates secures a quota of support. For a six member election the quota is one seventh plus one of the formal votes (disregarding fractional remainders). This is because only six candidates can secure such a quota, as the remaining votes would be just under a quota.

The normal result in a state is that the major groups (Coalition and Labor) win two or three seats each early in the count, but that allocating the sixth seat requires many counts (about 230 counts in New South Wales this year). The basic idea is that you first transfer the surplus votes, above the quota, of an elected candidate. This is done in Australia I believe by ttransfering all the votes at a fractional value (if the quota is 50 and a candidate has 100 votes then each is transferred to the next preference at a value of 0.5; so the winning candidate retains his quota of support and no individual voter gets more than the single vote they are entitled to). If there are no surpluses to transfer then the candidate with the current lowest vote total is eliminated (two Senate candidates this year only had one vote, an all time record) and their votes redistributed (at a value of 1 unless the particular vote was received at a fractional value as part of a transferred surplus, in which case it is transferred at that value). The process continues until a candidate accumulates the sixth quota. This can be someone from a major party, but often is from a party like the Greens.

The situation in Victoria is that a Labor candidate was a few thousand votes ahead of the Green for the last seat. Some Greens were asking for a recount (not a trivial matter when the paper ballots of an entire state would need to be looked at again).

Senate counts are time consuming, so it is just as well there are six months or more before the term starts.