Australia, like Italy and many other countries, allows you to obtain dual citizenship, therefore you may choose to have a dual passport.
So, how do you become a full-fledged Australian citizen?

If, as in most cases, you are a migrant, the first essential requirement is to obtain a permanent visa. This is valid for five years after which, if you still live in Australia, you will not need to renew it.
In order to obtain Australian citizenship, you must have lived in the country for at least four years under a valid visa and have had permanent residency for at least one year (inclusive). Be careful though, because in these 4 years you must not have spent more than a year in total outside of the country, as well as not more than 90 days in the year preceding the request.

Once you have obtained these necessary requirements, you will then be asked for the necessary documentation: photos, residential address, proof of your identity within the community and a copy of your birth certificate. Among the necessary documents there is also the criminal record that attests the total absence of convictions and pending cases with the justice system in your country of origin. But that's not all, because they will also want an identity declaration from you: you will need a person (necessarily an Australian citizen) to fill out a form for you and who must have known you for at least a year, confirming that you are who you say you are. This person must not have any family relationship with you and must be easily reachable by phone - they will call!

Are you already feeling tired just reading all these requirements?
No, come on, because once all your documents have been approved, all you need to do is take a simple exam that proves your knowledge of the country, its customs and its laws. The multiple choice test is held at the Immigration Offices and consists of 20 questions (to pass it you will have to answer at least 75% of the questions correctly). Once you pass the exam, you will be called for the citizenship ceremony, during which you will swear an oath of loyalty to the country, obtain a citizenship document and the right to vote.

The situation is more or less similar for those who marry an Australian citizen: you will have to meet the same requirements and still obtain a permanent visa in order to apply for citizenship.
Australia also allows you to obtain citizenship by descent, if you have at least one Australian parent but you were born in another country. In this case, you will not automatically become an Australian citizen, but you can apply through a special form.

Any non-citizen who does not have a visa to stay in Australia is considered an “unlawful non-citizen” and is liable to detention. This includes any person who arrives in Australia without a valid visa, a person who has had their visa cancelled or someone who has overstayed their visa.
According to Department of Home Affairs statistics about 1,500 people are held in immigration detention. While the statistics do not indicate whether or not a person is seeking asylum, we know that of these approximately one fifth were people who arrived without a valid visa.
Since July 2013, anyone arriving without a valid visa has been subject to the offshore detention policy in Papua New Guinea and cannot enter Australia permanently. Asylum seekers who are subject to offshore detention are not counted in the detention statistics reported by the Department of Home Affairs though.