Material is Candlestone, which is a corian alternative. I use both, candlestone seems to have a little more clarity, but another set of eyeballs may differ.
Both are available on ebay precut - I had a guy that was selling it real cheap, I'll post the info if I can find it.
Box is pretty easy, you can get as intricate or simple as you like. I usually use mdf and paint it, but occasionally like this one I'll use a premium wood for elegance.
Box is just 4 2.5 wide slats joined together with air staples. There is a formula that plays tricks with the mind [my mind at least] ... If your project is 8x8" and you are using .5 material, the 2 side slats must be a total of 1" longer in order to cover up the top and bottom slats. I use a table router to rout in a .25 slot in each slat, .25 deep, the corian will rest in and be secured by this these slots, and it will all join together perfectly.
So the formula would be 8+1", then - .5 to account for the drop in the slots, so it would be 8.5 for the sides. Top and bottom, you want it to come just to the edges of the blank to meet up with the sides, but once again you have to account for the drop in the slots, so it would be 8 - .5, they should be 7.5 each.
Doesn't always work perfectly but the corian itself can be adjusted via table saw to make it perfect, assuming you are under and not over in which case you'd have to cut new slats.
When everything is dry fitted correctly I use air staples to join them together with the blank trapped inside, 2 in each corner. Of course, you could use glue and clamp it overnight, or use any number of joinery methods to accomplish the same thing, but the staples work great, are quick and barely noticeable.
The back is nothing fancy, just .25 mdf cut to size and painted black on the outside.
for the lighting itself you will need a soldering iron, LED strip, controller and plug, also plug receptacle. I hesitate to post any source links and they most likely will not be valid in a few months, but all are necessary and all can be found on ebay ect as well.
I use plain white strips for these, no reason why multicolor could not be used, but I think most people would not care to see something like this green. I used to put the connector in the back, but now I put it on the side in case people want to hang them.
Note that I use hot glue to tack down the strip, I don't trust the sticky back LED to hold against gravity for any length of time.
Lighting itself is wide open to preference, incandescent/fluorescent can be used. Using just a lightbulb though you would have to think about light distribution and possibly heat buildup ,,, But there is no reason why you have to use LEDS, though I think for this purpose they are far superior to anything else.
here are a few pics and a link to an older thread with much the same topic, sorry if they are sideways I am getting sick and tired of rotating pics.viewtopic.php?f=16&t=21782&p=155568#p155568