Good, startoff with the Espressif sample project as a way to get up and running writing and reading a card simply. Supports 1bit and 4bit SD card interfaces.
The API provides functions that can read and write sectors directly if you don’t want to use the FAT filing system.
FAT Filing System
ESP-IDF uses the FatFs library.
However, it also supports the C standard library and POSIX API functions.