1. Getting an internship is hard work. You have to start early and work really hard at it. Research and networking both play important roles in getting you the internship you want.
I, for example, got my internship without the help of the Career Services department. I almost got one through them as well, but lost out in the final round because the company's plans changed (they needed someone immediately and I still had a month left in my study term) so they hired the other candidate instead. I talked a bit about using local job search engines, the library's resources, and blogs to carry out research and acquire industry knowledge (aside from using the the other, usual information sources, of course).
My classmates also talked about the extensive preparation they went through during their internship application process. This included getting others to read your resume & cover letter and practicing case interview questions.
2. Be realistic about your internship. See where you are now, where you want to be after you graduate, and then get an internship that puts you somewhere in the middle. If you're changing industries, be ready to work in a more junior position than the one you eventually want to be hired for.
3. Be strategic about your internship. Don't apply to every opportunity you come across. Pick and choose the ones you realistically think you can get -- or the ones you really, really want to get -- and focus on those.
Another important point that came up during the discussion was that the Australian definition of 'internship' is sometimes very different from the North American one. Here internships are often 6-12 month long work experience roles (almost apprenticeships). To do an MBA-style internships you may have to apply for a 3-month contract or short-project role (which, by the way, is what I did). Also, a lot of people (even those working in large multinationals) here don't know what an MBA is. You sometimes have to say "I'm doing a graduate degree in business. Could I do a short, three-month project for you?".
I spent the rest of my turn talking about my personal experience before I started the MBA (my background, etc.), a bit about my first two study terms, and what my internship was like (including a bit about which MBA learnings I got to apply in my internship). Overall, the career services panel sessions (there was an alumni panel that immediately preceded us) were really good. Here's hoping they take our advice and do a good job.