Interviewing a Game Designer is not an easy thing to do, especially if the Designer is relatively new to the industry. So, I thought I'd go over some of the things I look for in hopes that it will prepare new candidates for an interview process at a major game company.
The first thing I want you to do is show me your work. Bring any working levels you've built, dialogue scenarios you've set up, board games you have designed, school projects you participated in, etc. Showing physical examples of your work will not only prove that you are a capable designer, but hearing you talk through it will give me a lot of insight into how and why you designed certain things. Be prepared to talk bout all the planning up to implementation and precisely why you chose particular elements in the examples you are showing.
The second thing that I look for is "how do you fit in?" Adding a new Game Designer is like adding someone to our family. I I want someone who takes direction without being defensive, works well with others, thinks well on their feet, and isn't easily angered.
My last piece of advice is learn to think on your feet. I'm going to try and throw you a curve ball every now and then so get used to thinking outside the box because I want to see how creative you can be on the spot. If you have an example of your work with you, I'm probably going to ask you to do something like add a new feature that I come up with out of thin air. Design is not about quick decisions, So I'm not concerned with your actual answer as much as hearing you talk through how that feature would impact the entire game and how you would integrate it and compensate for it.
For general interview tips, check out Let's All Find Awesome Jobs by my buddy Kevin Fanning.