In the first place, remember that you should be professional. There are a number of people who track down video game developers at conventions to look for an interview, and this is one way to make sure that you never get a second glance. While it is fine to talk to a video game designer and while you are going to be in a place where you can share ideas and hear more about what they are looking for, remember that a convention or any similar situation like that is a poor time to start selling your resume. On the other hand, if you are at a career fair or they have an applicant’s booth, this might be a great opportunity to move forward and to make sure that you get their attention.
When you are thinking about getting a position with a video game developer, make sure that you are familiar with the games themselves. This doesn't mean just getting the top score in a certain game or being able to play it in your sleep. You should be someone who plays the games critically and who considers what other people are going to think about the game. This is far more than simply being a good player; you need to be someone who is interested in fixing the games, making it better and seeing what you can do with the next game! Development is something that definitely needs new ideas and you need to make sure that you are keeping this in mind.
Take some time and consider what your options are going to be when you are thinking about getting wok as a video game developer. Remember that there are many opportunities to get involved in the companies that you are most interested in, and one way to prove you familiarity with the game is to make sure that you are involved in things like beta testing and more. This will give you an idea of the kind of thing that they are looking for. Similarly, game testing, where you look for bugs, will give you a good background in how to figure out bugs and what you can do to move forward with the idea for perfecting a game.
There are many things to keep in mind when you are thinking about moving forward with video game jobs so see where your interests lie and what you can do!