The time required to apply for your student visa depends on a number of factors, including your nationality, travel history and time of the year that you are applying.
Australian Immigration provides useful estimates of processing times.
From our experience, the process can be as short as 5 days after you lodge your application. However if your case is complex, and if you are requested to attend an interview or submit additional documents, the process can extend to a couple of months. You will also need to have completed your medical checkup before the visa can be issued.