As noted, you'll need to write SPI routines to initialise and comunicate with any card, and you'll need FAT routines on top of that to read or write files which can be created or read using a PC. Getting either of those to work correctly will likely be a long, painful and frustrating process.
um..... slight understatement...
previous to my decent into lunacy while trying to get an sdinterface to work properly and reliably for almost a year!, i did have some limited and unreliable success with raw pics with initialising a card
contrary to what the sd standards say different manufacturers have implemented the standard in different ways with different tolerances to running voltages eg
some cards specifically want 74 clock cycles to clear the buffers in the card , some cards don't seem to care wether it's 74 or 90 and some want a specific number of cycles
then there is the operating voltage drama ideally 3.3v is what the card should be powered off but there are other problems some cards seem not to like.. eg noise, brownouts that you have to take care of as some cards will tolerate a bit of noise and others have a heart attack also some cards will run fine on as low as 2.5v and others won't
my best advice is to use a genuine sandisk card and follow the sandisk specs as far as spi goes
however there is TONS of information that the data sheets are missing that is relavant
