This a very broad question- "Native Americans" is a deceptive term, alluding to the false depiction of indigenous peoples of North America as homogenous, rather than the diverse groups that actually existed. There is also the question of traditional culture versus modern reality, especially with movements to revive and adapt traditional culture happening in many indigenous groups. A Daily Herald article from 2011 claimed that there were 562 tribes in America, and that's after hundreds of years of colonization and the implementation of federal recognition program. There were a similar number of tribes in Australia pre-colonization, over 500 with diverse language and culture. So, any comparisons made have to recognize the broad scope of culture within the framework of indigenous tribes.

There are many similarities, however, in a broad sense. Nativism, or a religious connection to the earth, is a common theme. Nomadism and hunter-gatherer tribal life, while not the only expression of society, was also very common. Oral histories were also important, storytelling defines the traditional knowledge that both Aboriginal Australians and Native Americans use to tell their own stories. Kinship is very important in both societies as well, elders are highly respected and the family group is tightly knit.

It has been largely believed that Aboriginal Australians were as a whole entirely dependent on their environment, and practiced no agriculture. The lack of agriculture is a benchmark for nomadic societies, it is not considered possible to be sedentary without it. The Coast Salish people of Washington State practiced what is called aquaculture—"fish farms" with defined strategies to used rivers and coastlines as set sources of food. Although the view of Aboriginal peoples as lacking this societal phenomenon is being challenged, for now it can be seen as contrasting culture to Native Americans.

Aboriginal Australians also broadly practiced circumcision as an important rite of passage, along with incision of the urethra. This is not generally seen in North American tribes, and in fact subincision ties heavily into sacred rituals. So although there are many similarities with ideas of self and connection to spiritual and natural forces, for Aboriginal Australians and Native Americans these ideas manifest differently in physical senses.

First, we should acknowledge that it is difficult to generalize about either native Australian or American peoples, who after all lived in a variety of different environments and developed very different cultures. Southeastern Indians, for instance, had far different lifestyles that were far different from those who lived on the Great Plains. But there are, perhaps, some grounds for comparison. 

First, most aboriginal Australians practiced hunting and gathering, which contributed to a very mobile society with a fairly egalitarian (equal) social structure. Not all Native Americans lived this way, but many did, at least at the time of European contact. The Micmacs, for instance, who lived in what is now Nova Scotia, collected shellfish, lobsters, fish, and sea mammals, a lifestyle which had much in common with people who lived along the southern coast of Australia and in Tasmania. By way of...