Submitting your taxes online is generally the fastest way to get your refund quickly. This year, you'll be able to choose from two different options: e-tax and MyTax.
MyTax is a newly-introduced option aimed at, in the words of the Australian Taxation Office (ATO), "streamlined online tax return designed specifically for people with straightforward tax affairs". Unlike the existing e-tax software, it's browser-based, so you should be able to use it on virtually any computer, tablet or smartphone.
MyTax works if you only have salary and wage income and deductions related to that income. There's a full set of questions on the ATO site which will tell you if you are eligible.
MyTax will be pre-filled with information from previous returns. One nuisance with that: according to the ATO, that full set of data may not be available until early August. However, if you're willing to fill out the date yourself, you can use the service from 1 July.
If your tax affairs are more complex but you don't plan to use an accountant, then the existing e-tax software (available for Windows and Mac) remains the best choice. This year's e-tax software should become available on 1 July from the ATO.
One big change that affects both e-tax and MyTax: you'll need to be registered with the government-wide myGov service (which also tracks interactions with Medicare, Centrelink and other services) in order to use it. You can register for myGov here.
Reminder: For specific tax advice relating to your individual situation, consult a registered professional.