You will need to register for many services. Registering in almost all services require a residential address and mobile phone number. So, the first thing you need is a confirmation letter with your physical address. One of the easiest ways to get this is to open a bank account. You need to physically visit a bank branch. After you open the bank account, they can issue a confirmation letter having your bank account details and your residential address. The bank does NOT need any papers to prove your residential address. They only need a valid passport. They take your words for it. Please, refer to this question for information about banks in Australia.
So, you need to find a place, which you can use as a residential address. Then, you need to get a mobile or landline phone number. Please, refer to this question for information about mobile phone service providers in Australia. After that, you need to register with a few authorities. Most government and private services are available online. To make it easier for you, the government created a website (https://my.gov.au), which provides a gateway to access several government services. It is highly recommended that you register on it.
So, here are the steps. Obviously, you need to have your passport with you when you visit these authorities. You can finish all of these steps on a single day, but you need to follow the steps in the order below. Some of cards can be received in a few days, but some might take 2 weeks to arrive. No cards are issued on the spot.
- Get a mobile or landline phone number. Please, refer to this question for information about mobile phone service providers in Australia. You can visit a mobile service provider store, or apply online.
- Visit a bank branch to open a bank account and get a confirmation letter having your bank account details and your residential address. Please, refer to this question for information about banks in Australia. You will need the bank confirmation letter when you visit the Medicare offices, and when you apply for a photo ID (or a driving licence.)
- Get a Tax File Number (TFN). Please, visit the Australian Taxation Office (ATO) website for more details (https://www.ato.gov.au/individuals/tax-file-number/apply-for-a-tfn/foreign-passport-holders,-permanent-migrants-and-temporary-visitors---tfn-application/.) You can apply for it online. The bank will ask you about this number when you open an account with them. However, you can inform them about it later (when you get it from the ATO.)
- Get a Medicare card. Please, refer to this question for more information about the health services in Australia. You apply for it online. While waiting to receive a Medicare card, you will have to pay the full price for the medical services you need. Make sure you get a receipt and save it. When you get your Medicare card, you can make claims for all medical services, which you paid for. You will need to submit the relevant receipts with your claim. Information about making claims can be found on the Medicare website.
- If you are eligible for Centrelink services, you need to register online. Skilled immigrants are NOT eligible for any benefits for the 1st 4 years of their residency in Australia. However, if you have children (in Australia), you might be eligible for some benefits. Please, visit the Department of Human Services website for more details (https://www.humanservices.gov.au/). Usually, Medicare and Centrelink offices are in the same location.
- Get a Photo ID. Yiu need to visit the relevant authority in your state/territory for more details. Usually, the road authority is responsible for issuing Photo IDs. For NSW, you need to visit the RMS (http://www.rms.nsw.gov.au/.) Instead of getting a photo ID, you can use your passport (and the bank confirmation letter for proof of residency) whenever a photo ID (or a driving licence) is required. Please, refer to this question for more information about getting a driving licence in Australia. Someone told me that in QLD 2 bank cards are required (1 bank letter is not enough.)
Note: If you change your address, you are required by law to notify several organisations. Please, refer to the following question for more details on this subject.
https://newaussie.com.au/categories/accommodation-housing/133-whom-should-i-notify-when-i-change-my-address