Step 1: Gather the Materials
A kindle case - I bought a $10 one from best buy
A battery powered reading light that you don't mind using up
Metal bars - To get power from the contact pad of the kindle (I used a pair of battery bars, got them off eBay or Amazon for $5)
Short length of wire - To connect the light to the metal bars
Hot glue/hot glue gun
330-Ohm 1/2 watt, 5% tolerance resistor from radio shack - optional to reduce brightness of light ($1.19)
Step 2: Make the Pads Useable
My final solution was to take my soldering iron, put just a bit of excess solder on the tip of the iron, a bit of flux on the pads, and after a second or two of touching the iron to the pads left just enough of a bump on the pads to make them useful.
For reference, when the back is showing the pad on the left is the positive terminal and the pad of the right is the negative terminal (this mean when the kindle is face up the positive terminal will be the one on the right and the negative will be on the left)
Step 3: Prepare the Light
One tip I would give on this that if you're buying a light just for this, try and get one that has it's battery compartment on the back side rather than between the light and clip. Mine had the battery compartment in this middle like this and I had to drill an additional hole through the clip so it would shut and turn the light off!
Once the wire is through attach them to the appropriate terminal. I would suggest doing this temporarily as after I had finished the project, I found that the light was getting too much power which would have shortened the lifespan of the LED, but more importantly annoyed my wife defeating the purpose of having a tiny reading light for my kindle in the first place!
The kindle touch provides ~5V @ 55mA through it's contact pads (or at least that's what my voltmeter said) I decided I want to lower this down to around ~10mA, it would dim the led and lengthen its life span back to normal. So to drop it from 55mA to 10mA I decided I needed a 330-ohm resistor... this might have been bad math :-P I'm no electrical engineer, but it brought the light down to the level I wanted to I count it as a victory!
Once you're satisfied with the level of light being outputted, solder the wires in place. I put a bit of electrical tap around the resistor to make sure there was no accidental contact with the positive terminal before the resistor.
In the photo below the reason it looks so messy is because I used some flux on the pads when I soldered it, but I didn't bother cleaning it up too much since it's hidden away and doesn't need to look nice.
Step 4: Prepare the Case
Also make sure to solder the wires to the metal bars before affixing them to the case as this is far easier than trying to solder them on *after* they're already in place on the case.
Measure out the distance from where your kindle will sit in the case to where you need to place the pads. Once you know where they need to be use the hot glue to affix the metal bar onto the case. Now I chose hot glue since I was dealing with a cloth case, but if you're using a different material be sure that hot glue will actually stick to it! If you have more skill than I do, you might want to consider trying to use some conductive cloth rather than the metal bars and wires as that would look more attractive.
Once the bars are in place, it's time to test it out! Place your kindle in the case and power it on (the kindle does not output power through it's terminals when it is in standby mode). If it doesn't work, check your connections and the placement of your bars. It took me a couple tries to get it just right.