I applied online and received an email within 3 or 4 days inviting me along to a group interview. You click on a link and then pick whatever time slot suits you.
The group interview had been a little awkward, as there were about 10 of us crammed into a small staffroom. The Area Manager interviewed us and began with ice breakers, where everyone introduced themselves and talked about what they knew about Aldi. This interview is basically a chance for them to see how you interact with others - so its definitely a good idea to be smiling and attentive and have a couple of questions prepared to ask the interviewer when they give you the chance. You don't need to chat the whole time, just look interested and happy and chime in every now and then and you should make it to a one-on-one interview. At the end he got us all to write down a few personal details, like availability and our locations, and then he got us to do 5 quick maths questions. They were simple subtraction and multiplication questions, with a trick question thrown in, "What colour are the Aldi uniforms?" It went for approximately 30 minutes.
I heard back in another 3 or 4 days that I had been invited to a one-on-one interview. Again you can chose what time suits you from the options online. Before this I had to fill out paper work for a police check and other safety information AND needed to get a medical assessment, which involved an eye test, blood pressure test, urine test, lifting weights, and then being prodded by a doctor and asked to do little physical tasks. The same Area Manager did this one-on-one interview, which went for about 10 minutes. He began by asking if I had questions about the group interview, then he asked me a few work and behaviour related questions. He then got the Store Manager to come over and she took me for a tour of the store, asking me what I knew about Aldi and if I had any questions, which only took 5 - 10 minutes.
Although I had thought it went well, I heard back in about 4 days that overall I was unsuccessful.