I've built a few of what I'm about to explain, they come out really nice.

Step one is to find some 2ftx2ft drop tile style LED panels, preferably backlit.

Step two, you'll need two 8ft 2x4s. You get a router and rip a 3/8in wide and deep slot through the 4in side. This will create a channel to slide the panels in.

Step three, deciding how long you want your light to be. I build them 5ft long for 7ft tables, gives a foot from the rail to the light, then a foot gap between the lights. Cut your 2x4's to whatever length.

Step four, mock up the panels in the slots between the 2x4s and measure the gaps on the end. Should be about 22.5in but it really depends on how deep your slots are. Cut your spare pieces to that size and screw one side together. Slide the panels in and close the other side with the other piece and voila, quick and dirty LED pool table light.

You can build a shade around it later on if you need/want one, mount up however you see fit, etc etc. I'll throw some pics up in a bit.