Watch the overview of the project and a description.
One a bandsaw or something similar, cut out your acrylic to the size you want for your sign. In this project, I used a rectangle of 6" inches wide and 5 7/8" inches tall.
You can carve in any design you like into your acrylic. It doesn’t need to be deep for it to light up pretty well. Even scratches can glow if they are deep enough! You can cut out a design in Easel, or you can do V-carving with software such as F-engrave. I used F-engrave and used a 90 degree 1/4" v-bit. I v-carved an image as well as some text. Be sure and reverse your image since you will be carving your image into the back.
I used inkscape to help align and position the elements in my carving and then used a g-code sender to carve those into the back of the acrylic. When carving, you will want a fairly high feed rate so you get good chip ejection. I used 50 inches / minute. Leave the paper on and engrave through it and remove it later when you are doing the final mounting.
In your walnut or other wood stock, carve out a slot to place the acrylic in and also hold the LED strip. Also, carve out a little pocket for the connector and cable coming off of the LED strip.
You’ve got a CNC machine – use it! Customize and carve in graphics, or text. Or whatever else your heart desires.
You can use any LED strips you want. Amazon and Inventables both carry tons of options. If you want to use the same ones as me (I wanted mine to be powered off of a USB port), I used these: http://smile.amazon.com/dp/B00PJWDM5Y
Mounting the LED strip is as simple as peeling off the adhesive backing and sticking it down. I used super glue to mount the acrylic to the wood but almost any method could work here.
Lastly, fill in all around the cable with hot glue to give it straight relief and keep stress off of the solder joint.