Step 1: Breadboarding
To get the rest of it, I bought up several fresh Jim-Packs of capacitors and resistors in useful-sounding values, opened up the National Semiconductor datasheet on the LM386, and started playing. When I got in trouble (which was most of the time) back-posts in random audio forums gave me new ideas to try. One of these led me to a zobel filter, and Wikipedia (of all things!) told me how to make a passive low-pass filter.
Okay, I still think you can do better with the same resources. There are lots of good circuit diagrams floating about the net. But here's my schematic anyhow (see below).