There is a vast amount of documentation available for embedded FAT file system implementations on removable flash memory. If the following links do not solve your problem, google for the exact problem you are facing.
SD Card Documentation:
Another SD spec sheet from ST Micro is here.
The SD card Product Manual v1.9
Simplified SD card Specifications (Does not include SPI mode details, unfortunately)
The official SD card documentation can be obtained here, the home of the SD CARD ASSOCIATION.
An app note for SD card interfacing in embedded systems
The MMC card Association is the body that controls MMC card technology.
MAXIM has useful information about interfacing SD/MMC cards here.
SanDisk MMC Specification in pdf format.
Paul Stoffregen has an excellent explanation of FAT32 documentation here.
FAT documentation from Microsoft is here and here.
Other interesting reading is FGA - Frequently Given Answers