Hi,
You should just put all the files in the archive into the root of a FAT formatted SD card (you might be able to use other formats, but FAT seems to work nicely across platforms). The .ext file is the root filesystem, that will be mounted during boot.
If you need to add stuff to the filesystem, you can either loop-mount this file under linux and copy files over, or you can simply put the files on the SD card root (or in a folder in the root) and then copy them over (or use them directly) when the Galileo is booted up, since the SD card root will also be mounted during boot.
No need to use dd or similar, simple copy will do, and the other files in the archive are also needed.
/Thomas