craftgrrl | How to cut/sew a "window" into fabric?

Hello, craftsters, and happy holidays! I just got a Kindle and I was hoping to make a cover for it to keep it pristine. I want to create a "window" with clear vinyl to protect the screen from scratches, with a fabric frame and background, but I'm still kind of a noob. My question is, how can I cut a square out of the fabric to make the "window" and sew down the raw edges to prevent fraying? It seems that cutting triangles out of the corners would still lead to fraying or an uneven/less-than-90 degree angle, as the inner most corners would not be folded over completely, if you get what I'm saying

Does anyone know of a tutorial for this? I tried searching Google, but I'm not quite sure what the exact term for this "window" is (I could only find tuts for curtains or peak-a-boo t-shirts). Would anti-fray glue hold up to continual use over time? I guess as a last-ditch effort I could cut out strips to border the piece of vinyl and sew them together, but I was hoping to keep the fabric in one piece. Are there any other suggestions? I hope I was clear enough, but if there's still any confusion I could try to draw up my design. Thanks in advance!