There are two national daily newspapers: The Australian, a broadsheet owned by News Limited, and The Australian Financial Review, a tabloid-sized business paper owned by Fairfax Media. The Australian is conservative and highbrow in tone (rather like its Murdoch stablemate The Times , to get an idea); the Financial Review is economically right-wing (so Americans, think of The Wall Street Journal).
Each of the state capitals has a daily conservative tabloid newspaper: The Daily Telegraph in Sydney, the Herald Sun in Melbourne, The Courier-Mail in Brisbane, The Advertiser in Adelaide, The West Australian in Perth, and The Mercury in Hobart. All of these, except for The West Australian, are owned by News Limited. Sydney and Melbourne each also have their own left-wing, somewhat more highbrow tabloid (formerly broadsheet): The Sydney Morning Herald in Sydney (obviously) and The Age in Melbourne, both of which are owned by Fairfax.
The two territory capitals have one daily newspaper each. Darwin has the Northern Territory News, a conservative tabloid owned by News Limited. The national capital Canberra has The Canberra Times, a center-left broadsheet owned by Fairfax.
There are smaller local newspapers, as well as national papers in languages other than English, such as the Italian Il Globo, but save for a few exceptions, these are only produced weekly and have low readership. There are also a variety of Australian magazines, such as the monthly Women's Weekly (work out the joke) and the now defunct news magazine Bulletin, as well as magazines from the United States, such as Time and from the Old Country, such as The Economist.
As the above quote shows, Australian readership levels are among the highest in the world. Actually, the national teams always ask for many newspapers to read as possible when abroad.
The Australian: Nation-wide, conservative, Rupert Murdoch paper for wealthy businessmen.
Daily Telegraph, Herald Sun, Courier-Mail, The West Australian, The Advertiser and Northern Territory News : These are considered to be slanted to the right of the political spectrum.
The Age, The Sydney Morning Herald and The Canberra Times: These are considered to be slanted to the left of the political spectrum.