Well, MMC and SD had the same serial interface till they stopped to develop MMC furthermore.
The SD-Cards today have a parallel interface to provide faster data transfer. However they
are backward compatible and support the old serial interface also.
Have a look at: SD-Card Wiki
Once you chose your cardtype it's juts upon you to interface it. There are lots of
examples out the net (Assembler, C,) and surely for BASCOM.
I don't know how to program in BASCOM since I use C and Assembler but have a look
at this: BASCOM-MMC
It's in german but the BASCOM-Library should explain itself.
If you want a more comfortable way to handle data on a SD-Card, you should
think about implementing a file system like FAT or FAT32.