The necessary parts for my cable won't be here until tomorrow, but here are the steps I have been able to glean from various posts on these forums:
1. You need a 1.8v TTL to USB cable to connect the small serial port inside your Kindle Touch to your computer. I probably don’t need to tell you this, given that you are a former technician, but others may also read this who are less tech savvy: it is important that you use a cable of the correct voltage or you might damage the serial port. Molex produces one with the model number TTL-232RG-VREG1V8-WE. A web search should reveal a few different places where you can purchase one. They are going for about $25 currently.
EDIT: yifanlu, who is far more knowledgeable about this process than I, says (in the next post below) that he uses a 3.3v USB to TTL adapter with his Kindle 4 and it works. While I obviously cannot confirm this, I bow to his expertise.
2. While there is a USB plug on one end of this cable, the other end is just the wires. Some people have had success simply holding the wires to the correct pins on the serial port. Others have soldered the wires to the port. A more stable, safe, and long-term solution would be to make a plug for that end. You can do this by purchasing small terminals (ends) for the wires that fit into a rectangular housing unit. Someone found that Molex also produces a housing unit (78172-0003) and crimp terminals (78172-0410) that fit the Kindle Touch serial port almost perfectly (certainly better than holding them by hand!). You should also be able to find these pretty easily.
3. The terminals in question being crimp terminals, you will need a crimping tool to use them properly.
Here is a detailed explanation of the overall process, along with some recommendations for tools. Apparently the custom tool you need to do this job properly is about $300, and there is the additional complication that the wires from the cable are of a lower gauge (and thus greater diameter) than the range given for the terminals (24AWG and 28-30AWG respectively). This may or may not matter. As I mentioned above, I am getting a more experienced friend to handle this part of the job, and this may involve use of a crimp tool and/or soldering iron. He says he will know when he actually has a look at the parts. (I will not be spending $300 to fix a device that I can buy new for less than half that price.)
4. It is necessary that the correct wires are connected to the correct serial port pins. If you open the back of the Kindle Touch and are looking at the serial port at the bottom the pins from left to right are TxD (transmit), RxD (receive), and GND (ground). One poster mentioned that on his cable the wires that needed to be connected to these pins were Orange, Yellow, and Black, respectively.
This datasheet (pdf) would seem to confirm that this is standard for this type of cable.
Others who have already gone through this process may want to add to or correct what I have written, but those are the details as far as I understand them at this point.