I know I have craft glue out but -- to be honest? -- I hate glue. I like crazy glue and hot glue and that's about it. White glue can jump off a large cliff and hit every rock on the way down. And, after a disastrous trial run with this project, I quickly abandoned the glue for scrapbooking tape.
I first tried glueing a 12 x 12 piece of cardstock to the background portion of the shadowbox. The result was terrible. White glue and I are just not friends. We gossip about the other to our mutual friends and we give each other the stink-eye at parties. We just don't get along. So, after scraping all of the cardstock and glue off the background, I used scrapbooking tape instead.
Now, I used a very simple cardstock background for my shadow box. I have patterned cardstock of all varieties, and it was tempting to use some of my more ornate patterns, but I decided on the most subdued pattern in my stack: a gray "textile" pattern (which I didn't take a picture of because I was too busy sending nasty emails about white glue). But the steps are quite simple: tape up the back of the cardstock background and press it onto the background portion of the shadowbox, making sure to line up each corner with the corner of the background.