The Arduino is going to remain unglued so it'll be easy to remove and upload new code. But since you don't want the connections to work free, it's not a bad idea to secure them with some hot glue.
Next, glue the LEDs into the foamboard. Be sure to follow the same layout as in the picture below! If they're installed in a different order, the animations won't work correctly.
Install the acrylic panel, glue the power jack in place and tuck the Arduino into its little cave.
Lastly, close up the back panel, apply a sticker and you're done!
Hang it on the wall, put it on your desk or give it as a gift! Every time you have more than a minute to watch it, you'll end up hypnotized by it.