I've already fielded enquiries from two people who have found my blog via Google, and given the 10,500 visas a year being issued, there's only going to be more, so in the interests of not spending too much time answering questions individually, I'm going to write a detailed account of things.
This article is not a replacement for doing your own homework. I expressly disclaim any responsibility for you getting your visa application denied, being cavity searched when you attempt to enter the US, or being sent to Guantanamo Bay. In particular, this information is subject to change, and as I'm not applying for a new visa every day, I'm not going to know about the changes. If you find something here that is blatantly wrong, or out of date, please let me know, but at the moment, I'm writing about my experiences. I'm undecided about maintaining a website devoted to capturing the state of the art in E-3 visa applications. If in doubt, spend the money (and I do mean spend, it's not a cheap phone call) and call the information line - 1902 941 641 - to speak to a human being, and ask all the questions.
Government's Department of Foreign Affairs and Trade's page on E-3 visas
Consulate's E-3 visa page
Consulate's page on applying for a non-immigrant visa
What's the process?
Your potential employer (sponsor) needs to file a Labor Condition Application (see the form here). At present, this form hasn't been brought up to date with respect to E-3 visas, it's the same form used for H1-B visas. Your employer needs to have written at the top of each page "E-3 - Australia - to be processed". This bit of handwriting is apparently key.
You need to have the signed LCA in your hot little hand before you roll up at the US Consulate to apply for your visa. As for how long these take to be processed by the Department of Labor, the FAQ says a week for postal applications. From my experience, and the experience of a couple of other people I've spoken to, it takes anything up to about four weeks. Generally speaking, you do not have to concern yourself with the LCA process, unless for some reason, you're sweating on the LCA so you can apply for your visa. My personal opinion is that the whole process is so long, bureaucratic and unpredictable, that you really don't want to be making any firm plans based on any assumptions on when you think anything is going to happen. Start your planning from when you have been issued your visa, not when you expect you will be issued your visa.
Once the LCA has been issued, your sponsor will send it to you along with a wad of paperwork, most of which you just take with you to the consulate. You can make an appointment online. Paperwork-wise, you need to take a completed DS-156 and a DS-157 if you are male between 16 and 45. These forms are available here. You can make an appointment online, the links to make an appointment at each of the US Consulates are also here. I found that the lead time to an appointment was around a month, so if you know the LCA application has been made, you can probably make the booking at the Consulate, so as to try and parallelise things a little bit.
What do you need to take to the interview?
You need to take your completed DS-156 and DS-157 forms. You need one for each person. So if you are the principal (i.e. the person being hired), you need a DS-156 for yourself, and your spouse, and whichever of you is male needs a DS-157. Bring the sponsor's offer letter too.
You need a receipt for a non-refundable visa application fee. You need one receipt per person applying for a visa. You get these receipts by paying $130 per person at any Australia Post outlet.
As the visa is non-immigrant, you need to be able show some sort of ongoing connection with Australia. If you own property here, and are planning to continue owning it while in the US, bring a rates notice. I don't know what else is useful to demonstrate an ongoing connection.
Also bring a bank statement, as you need to demonstrate an ability to support yourself while in the US.
Bring birth certificates and marriage certificates. Also bring a copy of your University transcript, and any assessments that your employer may have had done that state that you hold the equivalent of a US degree. I'm not sure how hard and fast the whole degree thing is. I have an incomplete degree and about 10 years of work experience. This was sufficient. I don't know how you'd go with absolutely no degree and lots of work experience.
Finally, you need to bring two US-sized passport photos. These are 5cm x 5cm, which are not what your average passport photo is like if you go somewhere and ask for a passport photo.
Processing takes about 3 days, although you get an indication on the day as to whether you are successful or not. If you don't want to come back to collect your passport with the visa in it, you need to leave sufficient stamped, self-addressed envelopes so that the Consulate can mail the passports back to you. It's a bit hazy as to what constitutes 3 days, but assume 3 full working days, plus whatever time it takes for the postage, so up to 5 working days.
Good luck with your visa application. Let me know how it goes, and if this has been of assistance.