Interfacing microSD with LPC1769 Board
From nxp.com: AN10916 - "FAT library EFSL and FatFs port on NXP LPC1700" should give you some pointers. 

There is also AN11070 - "Accessing SDC/MMC card using SPI/SSP on LPC1700".

The specifications for SD(-HC, -XC) can be downloaded from sdcard.org.


  how to properly incorporate it into the C compiler for the board


We don't know which compiler or board you use.