Most later PET's had a little piezoelectric speaker built-in. You can use PetSynth right away without any hacking. Mic it for an authentic old-school PET sound.
However, if you want to, you can add a wire and a little capacitor (for coupling or play is risky and straight-out leave it out) and plug right into your mixer.
Just wire up the speaker wire to a capacitor marked has "104" or so (you want a .1 uF or similar, probably 0.01 is fine) to the speaker connection on the PET mainboard on one end, and your wire to your mixer on the other.
Please note, the PET wasn't designed for sound, never mind this. Although the capacitor above is there to avoid damage to the PET through blocking DC, as well as trying to protect the mixer, I've notice mystery sound levels on my mixer when recording. It looks like there's DC offset or something, but I'm not sure. Use at your own risk!
I'll add so pictures and instructions in the future showing how I did it. However, I only did what works for me - although it's been fine for a year, you should probably be careful or consult a better resource than I. It would be crappy if you let out the "magic smoke" of you beloved old PET. Or worse, the built in sound card chips on your laptop!
In fact, I highly recommend you don't plug this setup directly into your computer or laptop unless you've got a cheap, external sound card. For example a cheap USB or PCI based sound card. Again, it's been fine for me, but I've been outputting to a little Mackie Mixer and then to a USB M-AUDIO device.
Also, the PET output is LOUD. It's NOT line level. It's not even comfortable headphone level. It's loud enough to drive a large piezo speaker on the mainboard. Since there's very little background noise, it's hard to tell how loud it's going to be.
Again, be CAREFUL! The safest thing you could do is mic the PET. I would feel badly for you if you damaged your PET or other gear.
Remember, deaf ears make for short careers! Protect your hearing first, your gig second, and your gear last. You can always by new gear, but you can't buy new ears, or gigs!
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Or, there's another way, but I haven't tried it. You get an edge connector for the PET parallel port and a few resistors and plug the other end into your mixer. There's a diagram on the opening screen of the SPACE INVADERS game for the PET I'll add. Maybe I'll even try it someday and let you know how it goes.
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Stay tuned - I will research sound output and recording on the PET and try to put something together with a little more details once I have some more information.