First step is for the company is to get approval to sponsor the training visa 407 if they haven't already. This process takes anywhere between 3-6 weeks. Once approved they then need to nominate you. Before they can do this they need to do the mandatory skills analysis to ascertain the required training to bring you up to the Australian Quality Training Framework (AQTF) level for the occupation in which you are nominated. This is usually a certificate IV level but not always, it depends on the occupation. Once the analysis is done, the skills gap is then transferred to a structured and tailored training program, designed in a way that increases in intensity as you advance through your visa period. This process is critical as it can be the success or failure of the visa. It must be able to justify to the government that there is a need for training and not just a less expensive way around the 482 visa and skilling Australian fund. Because of this the government have clamped down on this category in recent times, so I cannot stress enough to ensure your company gets the process right. Once the program is designed it is submitted with the nomination, which then matches-up in the system with your application. Then it’s a wait period of anywhere between 6-12 weeks (Being from UK it is likely to be the lesser end of the time frame).
Processing times are here.