I remember reading the schematic for this board (long time ago now) but I don't have one.
As far as I recall the board has a huge configuration space (mostly managed by solder bridges, but there are a few DIP switches too) meaning there's a good deal of flexibility on how the base board and the mezzanine can communicate.
On most cases reading a sensor means writing firmware code for the STM32 to read the sensor values and make it available to the base board. Again there are many ways to do this and it depends on your goals, additionally some of the sensors are connected directly to the base board (if the DIP switches are set correctly).
However if you are just getting started and need to build up experience, one of the simplest things to do would be to create a program for the STM32 consisting of a loop that continually reads sensor values and then sends them to a serial port (perhaps with a 1 second sleep to prevent too many readings coming in).
Which sensor is your first priorirty?