data transfer by MISO?

I have a BBB running a number of fast analog to digital chips. The circuit designer (who, sadly is now very ill and has retired from the fray, has provided a number of MISO lines each connected to an AtoD output. How can I read these output values back into my C code?

You haven’t provided many details.
If you’re simply trying to get the value on a specific gpio pin, you can do so by reading it from a file in:
/sys/class/gpio/gpioX/value