Hi Cabe,
This IC runs the speaker in a differential or bridge configuration, that's why it can get away with not having a DC blocking capacitor on the speaker. If you want volume control I would recommend to replace R1 with and appropriately valued potentiometer and take the signal input to the chip from the wiper. Due to the amplifier's configuration I wouldn't add the pot on the speaker end, you will get better performance if you add the volume control near the beginning of the signal chain were currents are generally small and little noise will be created by the passive components.
hth,
Jorge Garcia
What do you recommend as a simple way to adjust power at the speaker?
Typically the pot would go on the input. One side to GND, one to the input signal, wiper to the amplifier chip.
For example http://audio-circuits.blogspot.com/2011/03/1w-mini-amplifier-circuit-based-tda7052.html
I was thinking of adding some further amplifying stages after the IC.
An "audio amplifier" is essentially an output stage. If you need additional amplification due to low input signals, you'd add a pre-amp at the input using a different "style" of chip. If you need additional power overall, you pick a different audio amplifier (which will usually require more battery power, since "theoretical maximum output power" is directly related to input voltage. There are a lot of "audio amplifier" chips out there; is there a reason you're focused on the TDA7052? Nowadays I'd be thinking about the "class d" chips like the National Semi (TI!) http://www.national.com/mpf/LM/LM4667.html#Overview (may not be very hobbyist-friendly, packaging-wise.)
I have tried to buy the little guitar amplifier off of various gadget websites, with no luck.
The little boxes widely sold as iPod speaker/amps have been looking like widely applicable general purpose battery powered audio amps to me, recently. Price and "quality" go from low and adequate to pricey and "audiophile", in a wide variety of styles. For example http://www.amazon.com/PA-219-Foldable-Speaker-Battery-included/dp/B000CSVMJ8 I don't know whether they're compatible with guitar outputs.
Help me with my op-amp issues, and you will have it figured out.
http://www.element14.com/community/message/38219#38219/l/op-amp-differential-to-single-ended