My hobby / project is a 6502 homebrew machine with video (TMS9918), sound (AY-3-8910) and relevant for you an SD Card interface driving a hobbytronics SD card breakout board. This simple but compact board provides a slot for a micro SD card, and exposes the lines needed to drive the SPIO interface (CLK, DO, DI, CS, CD). The SPIO lines are connected to a 6522 and so all transfers are bit-banged in software. Not massively fast but still getting around 8.5k per second which is enough for my needs.
https://hackaday.io/project/5789-6502-homebrew-computer/log/26703-sd-card-interfaceMy main site includes the sd card driver code, but also the FAT16 routines which are much more complicated but allows a standard PC-DOS format to be used which can be helpful in portability.
Hope this helps.