This is a difficult road to get on because there are so many who also want to do this. I myself am trying to get an internship as a game designer. What you should start doing is trying to get into game betas. Once you are accepted into betas you should work really hard to try and find the bugs in the game and submit them.
Being a good beta tester for quite a few games will help you to both get invited to more betas by the same companies and will get you on track to possibly get a job as a tester. Just be sure to work hard and brush up on your programming languages as while they may not be necessary for all design jobs in the video game industry it is always a plus as it is such a crucial part of the development process.
Good luck to you and just be sure to work hard and don't give up.