It is advised to ask for your visa at least two months before your departure. The sooner is the better.
For a temporary travel in Australia, there is different kinds of visas :
The Students Visa: You will have to prove your enrolment in an Australian university. Your financial situation may also be checked at the Customs in order to be sure that you will be able to afford student life. You will have to be a full-time student, but this Visa also allows you to work about twenty hours a week. It also exists Visas for professionals or students who want to do a training in Australia.
The Tourist Visa: For the people who wants to visit Australia for a holiday or familly. Customs may check if you have the funds to buy a return ticket.
The Working Holiday Visa: The Working Holiday and Work and Holiday programs encourage cultural exchange and closer ties between arrangement countries by allowing young people(18 to 30) to have an extended holiday supplemented by short-term employment. You will be allowed to work for up to six months for the same employer. You can study for a maximum of four months. This Visa allows you to stay 12 months in Australia, but you can ask for a second Visa of the same length. Like for the other Visas, you will have to improve you have necessary funds on your account. The Visa is valid one year since its creation.
Other Visas: many other Visas exists, you will find with all the detail on the Australian website for immigration.