Check out the garden area on the wiki
http://stateofdecay.wikia.com/wiki/Garden_Area
I've never made one personally since I seem to always have too much food, but they can only be built in "outside" slots at your base.
Yeah I know, but I don't seem to be given the option to build one.
There doesn't seem to be a requirement other than to have an open slot outside. I've had the build icon pop up in my game in a fresh base. Perhaps you need a workshop first. Do you even have the red version of the icon show up? It's an icon of a wheelbarrow.