Note that the flickering of the leds is not as noticable in real life as it is in the video. This is due to the PWM of the lights being off from the camera rate.
This is fairly easy to build as long as you have patience. Although there is a lot of soldering, it's easy to do on the strip board. I recommend having some programming experience if you build this.
You will need:
A controller - I used an LED-Wiz. I plan on switching to an arduino later, but this got me up and running quickly and easily. This controller is capable of driving 32 channels at 500ma, since each led requires 3 channels at 20ma (Red, Green and Blue) this gives me support for 10 light bars with 25 led's each (500ma / 20ma = 25 led's).
RGB Leds - I bought a pack of 200 off ebay for about $65. They are poor quality and there's some variance in the color between them but they were cheap and do the job just fine. I chose to go with 10 bars of 19 leds to give me a few spare led's in my pack. The ebay auction I bought had the title "200X Diffused 5mm Common A Manual Control RGB LED 8Kmcd"
Stripboard - I found stripboard at my local electronics supply store for $6.
Some other people have found it online here:
Resistors - See Below
Wire - I used ribbon cable from my local store, it came in a 20 wire width which i tore into strips of 4 wires.This is the same type of cable used in floppy drive and ata33 cables.
Mounting hardware - I used vinyl siding from Home Depot, see step #5
Power Supply - You may be able to use your computer, see step #6
Software - See step 7. A computer is REQUIRED and the ambilight effects will only work with video being played from the computer. Unless you are using a video capture card to watch TV, it is not possible to have the effects from another source.
Calculating the resistor sizes:
The easiest way to figure it out is to use the online calculator here. My led's were listed as being 20ma forward current with green and blue at 3.6v - 3.8v and red at 2.0v - 2.4v.
Open the calculator and click on "Parallel leds" at the top. Entering 5 for supply voltage, 3.6 for voltage drop, 20ma for current and 19 led's gave me a value of 1 watt 3.9 ohm. Notice that the red led is different so it requires a different resistor.
The store I was at did not have nearly enough 1 watt resistors so I decided to just go for 500mW ones instead. The calculator says the resistor dissipates 503mW in my situation so I should be safe and thus far they have been reliable. I do not necessarily recommend this approach.
If you have questions about the build, please post them as comments instead of messaging me. I've received many questions that are similar and if they are posted in the comments it allows others to learn from them as well.