Before federation, each of the six colonies had its own constitution. These constitutions regulated, among other things, the Legislature, the Executive Government, and the Judiciary of the States. The Australian Constitution expressly guarantees the continuing existence of the States and preserves each of their constitutions. However, the States are bound by the Australian Constitution, and the constitutions of the States must be read subject to the Australian Constitution (ss 106 and 107).
In contrast to the Commonwealth Constitution, the State Constitutions are in general, simply regular pieces of legislation that are subject to amendment or repeal by the State Parliaments in the same way as other legislation. The State constitutions are the source of the State parliaments' power to make legislation and are concerned with the structure and process of the institutions of government: the legislature, executive and the judiciary.
The official versions of State Constitutions, as passed, as amended, point in time and current compilations are available on the respective states' government legislation websites.
The current compilations are:
The position of the territories is different - they do not have constitutions as such. The Northern Territory and Australian Capital Territory (ACT) were granted self-government by the Commonwealth in 1978 and 1988 respectively with the passage of Commonwealth legislation: the Northern Territory (Self-Government) Act 1978 (Cth) and the Australian Capital Territory (Self-Government) Act 1988 (Cth). These self-government laws are the source of the ACT and NT parliaments' law making power, and are structured similarly to the State and Commonwealth constitutions, with chapters on the functions of the Legislature, the Executive and the Judiciary. Territories can make laws for any matter as long as it is not inconsistent with a Commonwealth law made under s 51 of the Commonwealth Constitution.
See also the chapter on State Constitutions in the following book:
Powell v Apollo Candle Company Ltd (New South Wales) (1885) 10 AC 282;  UKPC 5 - this Privy Council decision dealt with the powers of colonial legislatures. It decided that colonial legislatures, though subordinate to the Imperial Parliament, were not mere delegates and were empowered to delegate legislative power to the executive.
McCawley v The King  AC 691; (1920) 28 CLR 106;  UKPCHCA 1 - this Privy Council decision concluded that the Parliament is legislatively sovereign. This essentially has been the basis for all subsequent State constitutional law in Australia.
Attorney-General (NSW) v Trethowan (1931) 44 CLR 394;  HCA 3 - this case, on appeal from the Supreme Court of New South Wales, concerned the Constitution Act 1902 (NSW) and revolved around the Premier of New South Wales, Jack Lang, and his attempt to abolish the New South Wales Legislative Council. It was found that the Legislative Council could not be abolished by mere legislation, but rather there is an entrenched requirement for a referendum to precede any such abolition.
Clayton v Heffron (1960) 105 CLR 214;  HCA 92 - this case revolved around whether there was a requirement under s 5B of the Constitution Act 1902 (NSW) that a bill to abolish the Legislative Council, twice passed by the Legislative Assembly and rejected by the Legislative Council, required a free conference between the houses first before being put to a referendum. It was held that it did not.
Kable v The Director of Public Prosecutions for New South Wales (1996) 189 CLR 51;  HCA 24 - this case is about Chapter III rights in the Commonwealth Constitution and the scope of power of state courts vested with federal jurisdiction. It restricts the power of State Parliaments to control the activities of State courts.
Arena v Nader (1997) 42 NSWLR 427;  NSWSC 468 - this case revolved around the validity of legislation providing for the waiver of privilege by a House of the New South Wales Parliament. Both the NSW Supreme Court and the High Court found the legislation to be valid.
Egan v Willis (1998) 195 CLR 424;  HCA 71 - on appeal from the Supreme Court of NSW, this case concerned the Constitution Act 1902 (NSW) and confirmed that the Parliament has the power to call the Government into account. This is the principle of responsible government. The Government is answerable to the demands of Parliament. This principle was confirmed in the subsequent case of Egan v Chadwick (1999) 46 NSWLR 563;  NSWCA 176.
Source: George Winterton (ed) State Constitutional Landmarks (Federation Press, 2006)