Simple amplifier circuit for a synth chip
Appendix C at the bottom of the datasheet link is the Typical Application Circuit.

(source: waitingforfriday.com)
Notice the top right corner listed Audio out. That's the typical circuit needed, just a 1kΩ resistor, and a 1µF electrolytic capacitor (and a plug connector). As a 3V peak to peak, basically a strong line level, it can plug into most stereo line ins, and it should drive headphones directly in an okay manner (mono of course).  You shouldn't need anything else, but I suggest using a pair of dollar store headphones first.