1. Figure out the size.
Again, you can make it as big as you want, but a grid of 9 pixels is pretty manageable for a first try:
Mine consists of an 8" square with nine 1" diameter circles arranged a grid at 1-1/8" from center to center.
2. Laser-cut your shape out of a sheet of mirrored acrylic.
The circles cut out of the center will be used as the face of the pixels. I used circles to avoid trouble later on in orienting and aligning them.
3. Put some rubber on the back.
The black rubber shown is 1/4" neoprene sheet. Cut out a 6"-7" square of it, at least big enough to cover all the holes. Super glue it onto the back of the panel. The neoprene is what the pixels will eventually be attached to, and seems to do a pretty good job of holding them firmly while not dampening the vibration.
4. Make a frame.
If the thing stands up on it's own, everything will be a little bit easier. To this end, I built a wooden frame for the panel to mount to . Make it deep enough to mount the Arduino uno board inside, around 3". For more details, maybe find a woodworking friend, or find a wooden box the right size, or make one out of cardboard, or macaroni.