Looking at the larger setup: The arduino records 10-bit analog at ~10KHz, for <5KHz bandwidth. There will be pauses in the sampling as the SD card is written to.
Will those limitations be okay?
Connect it up per page 12 of the data sheet.
Power is 1.8V.
Clock speed - typical is 2.4MHz. If you use SPI at 1/4 processor speed, that is 2MHz.
You will have 512 bytes of data every couple of mS.
SD uses SPI to write data to the card.
You can try a loop to read the data
for (x=0; x<512; x=x+1){
dataArray[x] = SPI.transfer(0); //MOSI connects to nothing, MISO connects mic data pin, SCK connects to mic CLK pin
}