To decode what the remote was sending, I used an oscilloscope and a small photodiode. The photodiode generates a small amount of voltage when light hits it, and responds to changes in light level quickly enough that the oscilloscope can draw a really nice plot of the signal. I have a Parallax USB oscilloscope, which is perfect for showing the command pulses and is just fast enough to find the modulation frequency. As an aside, I’m really happy with the Parallax oscilloscope for projects like this. It is simple to use and I love being able to save images to share with people.
Here’s what two of the commands from the dimmer remote look like. The top signal is the “fade lights up” command, and the bottom one is “fade lights down”: