I conducted mine with a Supply Corps O6 in August 2013. The interview lasted approximately 30 minutes and there is a form they largely go off. We chatted for a little while about common interests (sports, etc) and then the Captain basically had me fill out my form verbally. I spent about 10 minutes asking him questions about the Supply Corps that I couldn't easily find the answer to online, and at the end he mentioned he would give me a good recommendation.
There were two points where I realized a military interview is not really much different than a civilian interview. First when he questioned why I did not leave law school if I was not going to become an attorney (sunk cost thinking, etc) and second when he asked me to provide 3 words that would describe myself. I provided 3 sentences, which he politely reminded me was not what he asked. One of those moments where you internally /facepalm. These questions were questions I've seen in interviews on the civilian side more or less, so there's no special handshake or anything to this interview.
I wore a dark suit and a red tie. I strongly advise you wear a suit, as this is a job interview.
The questions I asked were basically:
1) What type of advanced degree is currently sought after, and in his experience, what is the best way to go about getting it? i.e., Should you go get that Petroleum MGMT degree, go the Navy-paid top 30 business school route, attend a war college, or do your MBA at night classes during shore duty so you can still get FITREPS while your peers are not getting FITREPS.
2) How many supply officers reach the brick wall of non-select for O5 at years 13-15 and are shown the door, close to retirement?
3) What is the most important lesson he learned/kept from his time as a JO?
You get the idea. I don't think using this time to ask silly questions like "What's it like being a Supply Officer?" is really a good idea, but that's your call.
Good luck, and take my experience with a grain of salt. YMMV.