The LEDs will be mounted in foamboard (or posterboard) just inside the back panel. If you're using a purchased shadowbox, it will come with a panel for mounting the display items (probably covered in cloth). Remove that panel and cut a piece of foamboard to replace it.
Don't glue the Arduino down. It needs to remain removable so you can plug in the USB cable and upload code.
Take extra special care to measure very carefully when cutting these holes! A crooked line or sloppy cut will put an LED (slightly) out of line and will be VERY noticable in the end product.