Here are some schematics I've pulled out of the TR-808 schematics. I didn't do the bass drum, snare or hihat since ericarcher.net has already done a way better job than I could with that.
Inspired by him I've so far made veroboard versions of the bass drum, snare drum, the three toms and the cowbell.
I'll post those layouts once I'm done with layouts for all the sounds. Not sure why I'm posting this, but, eh, why not.
So, yeah, Here's something:
The toms/congas use pink noise from the noise generator.
The snare uses white noise created by the same circuit.
These last two also uses a schmitt trigger. Look up the original schematic and you'll figure it out.
But it looks like this: