Depending on the compiler you use, you can find full SD support libraries that will make writing to FAT formatted SD card a breeze, and you can even do the USB thing if you desire but it's not as simple...
The Mikro compilers have SD routines built in, there is an excellent library for Swordfish as well as a few 'generic' libraries that are cross platform... I'm sure other compilers have built in routines as well I'm just familiar with the ones I suggested as I have played with them...
Can't or don't want to deal with writing the access routines or using a compiler I can't recall the name off hand but there is a simple serial controlled chip that has a full compliment of DOS like SD access commands and controls... If I remember correctly it's a little costly but damn simple...
**EDIT** The interface chip is called ALFAT SoC Processor, supports USB as well as SD but it's a little costly IMO unless it's a one off design...