While I've been waiting for the go-ahead on my roughs, I've put together a few tips about what to expect if you are successful in getting an appointment with a publisher.
It's not like a job interview, so you can put away the suit. Dress normally, but just make sure you are neat and tidy (no ketchup stains on the T shirt...) so you look like you made the effort.
Well, it normally lasts 10 - 30 minutes, depending on how busy and how interested they are. They will look through your work and ask you a bit about yourself. It's generally very informal, so try to relax and just be yourself. Be enthusiastic and friendly though. And remember to smile...
You are still one of many illustrators they will be seeing that week, maybe that day. It is vital that you do not just become a blur with all the others. If you can think of a way to be memorable (in a positive way of course!) that's got to be good...
People ask me if they should get an agent to do all this for them. My advice would be no, not yet. You can learn so much in the early stages from meeting art directors in person and listening to their feedback. Also, until you are published, it can be just as hard to get decent agent as it is to get a publisher - they too are swamped!
If you found this useful, there is also a fair bit of detail about publishing, from an illustrator's perspective, on my blog posts over the past 18 months. It's all hopefully interesting and relevant stuff, but if you want specific advice, here are my hot tips posts.
Plus, don't forget, there are also the videos on my website, talking about how I got started as an illustrator and showing some of what I do.
Now: go knock 'em dead!