I have the zip downloaded, but it just looks like the blender folder (the one in program files), and not like a common addon. What do I do?
The fracture modifier project is not an addon, it is a development branch of blender that adds the fracture modifier as a core feature within blender's source code and aims to have it incorporated into a future blender release. You need to use a copy of blender that was built using the separate branch of development.
The site you link to includes downloads of pre-built versions of blender which include the fracture modifier. If the available versions don't work on the system you have, then you will need to build your own copy of blender by checking out the fracture_modifier branch instead of the master branch.