The DS-160 is the application form for a US Visa and gives the US Government a complete background of you, and gives them everything they need to interview you for your visa. This document is somewhat generic and applies to lots of visas but contains a lot of information in it, so be careful!
The DS-160 will ask for a location on it, so it's important that you select the same location in that, as the location you pick to do your interview. If you need to change the location of your interview after doing your DS-160, my recommendation is to do a new DS-160 and then update the consulate (either online through the portals below, or by contacting them directly). If you can't get in touch and update it, just take both printed out confirmation pages and explain the situation. You should be fine (but don't rely on having ONLY one with the wrong location on it).
If you get things wrong in this document you'll have to do it all over again, which is a monumental pain. To start the DS-160 you head to this official Government website (and never anywhere else). The website is awful, and it will constantly crash on you so I highly recommend saving on every single page, and every single time you insert any information. Chrome seemed to work best and definitely don't do this on your phone.
If this is your first E3 visa application, it’s recommended that you do your appointment in Australia, but you do not have to.
When planning this trip, remember that the appointment wait time estimates on the US State Department website are for US citizens and are wildly inaccurate at that. You, as an Australian are a “third-country national” (First is the US, second is the country with the embassy/consulate and third is you).
Each consulate has a specific number of slots for these kinds of appointments, so the wait times could be very different than those estimates. You can and should, however, take the listed processing times into account.
To book your appointment, there are two major websites that you'll be directed to, and which one you use will depend on where you're headed for the appointment: http://ustraveldocs.com/ and https://ais.usvisa-info.com/. I haven't found a clear way to define which one is which but if you browse through each, you should find the country you plan to visit and links to their booking page (not their Embassy page).
These two websites are the portals to booking your appointment and will take payments and track your progress throughout.
You create an account, select a location, and then proceed through the steps that it tells you. It likely tells you to start with a DS-160 because that's your ticket into getting an interview. You will then have to pay a fee to see the available appointments. This fee is non-transferable to another location and you can't see the calendar of available appointments before paying. It's a huge pain, but you have to take a bit of a gamble and just push forward.
Once you pay you should be presented with a calendar of options. If there are no appointments available it means that all the appoints for the next booking period (normally a couple months) are booked out. Keep refreshing this page all the time and you will likely see an appointment appear as somebody else canceled. Otherwise you will just have to wait until you see a spot open up.