You'll have to wait to show your friends until the release of the game. Many times they'll send you a free copy of the game when it's released, or other rewards such as a T-shirt. List previous games you've tested and what you plan to do as a tester. You must be willing to devote hours of your time to help with testing. When I was accepted to my first closed beta, this helped me get into other closed betas, which in turn, helped me into other closed betas, until I can make a whole list of games I've tested for experience.
Beta testing is like proofreading a paper.
For some reason when you proofread it by yourself, you tend to pass up a lot. That's why I try to have a friend proofread it also because they'll have a fresh look. That's why it's important for you as a designer to get multiple testers on your project and for you as a tester to catch these bugs and report them. Testing isn't all about technical errors though. It's also about enhancing the game - making it look better, sound better, and be more fun.