This tutorial provides the basics for using a WIZ5500-based Ethernet Shield with an Arduino compatible.
When the original tutorial for using the Ethernet shield and sketch was written 7 years ago, serving files via Ethernet was pretty novel (read: wicked). Ethernet shields are not as common now. It is likely due to the proliferation of Wi-Fi boards.
Hopefully this updated tutorial will give you the basics for using a microcontroller to access an SD card (or something else) via Ethernet. The same methods can be used if you wire up a SD card breakout to the your microcontroller pins, just be sure to check for any necessary code changes.
More Information : https://learn.adafruit.com/arduino-ethernet-sd-card?view=all