It's somewhere in between easy and hard. There are two ways to do it:
a) Prepare the card on a PC, then replace it inside the Zero.
Download the flash images from the flashing page
. Also download the "assemble_images.sh"
Rename the flash images to the way the script expects them (basically, remove the dates from the file names). Then run the script to generate the single "sd_image.bin" image. The script requires some basic UNIX command line tools; it is tested on Linux but it should run in other environments as well, for example MSYS or Cygwin on Windows.
Finally write that "sd_image.bin" image to the SD card, using a raw sector writer. The latter is important: if you just copy the image file to the card as a file it won't work. Programs to do this exist on every OS; on UNIX you can use the command line tool "dd": "dd if=sd_image.bin of=/dev/<block device of the SD card>". Make sure you select the right target device; writing this image over your hard disk is a Bad Idea.
b) Replace the card inside the Zero, then reflash the Zero.
Follow the instructions from the flashing page
. This requires a Linux PC.
Replacing the card requires opening the case just a bit. You only need to unscrew the four screws on the back, then very carefully move the back a bit so you can access the internal SD slot. The wires of the battery and especially the vibration motor can break if force is applied to them. When putting the unit back together, make sure no wires are caught between the case halves.