You'll need a socket to plug your SD card into. I bought these simple microSD adapters from a popular online marketplace:
There's not much logic on the board itself, just a 3.3V regulator and an IC to level-shift between the SD card's 3.3V signals and your computer's 5V TTL-compatible signals.
I've also used a microSD socket that's mounted on the back of an LCD "shield" module designed for Arduinos - the details aren't critical and there are a lot of options out there.
Some adapter boards (though not mine) provide a signal to tell you whether a card is present, which you might find useful.
I'm not the first to do this, of course! 6502s and SD cards have been around for a long time and you're sure to find a lot of good examples if you search, especially on places like hackaday.
Wikipedia has a good reference for basic SPI communication: https://en.wikipedia.org/wiki/Serial_Peripheral_Interface
The following document was extremely useful regarding how SPI applies to SD cards, how to send commands, the initialization sequence, and what all the commands are: http://elm-chan.org/docs/mmc/mmc_e.html
You can also download the Physical Layer Simplified Specification from https://www.sdcard.org/downloads/pls/. I did, but didn't refer to it much.
As usual there are also many discussions on 6502.org.