Save the zip file somewhere on your computer. You may want to rename the file to import-daz.zip, but it is not necessary.
Blender 2.79: Open Blender and the User Preferences window (File > User Preferences). In the Add-ons tab, press the Install From File button.
Blender 2.8x: Open Blender and the User Preferences window (Edit > Preferences). In the Add-ons tab, press the Install... button.
Navigate to the zip file you just stored and press Install from File...
You can now enable the add-on by clicking on the checkbox to the left. Press on the arrow beside the checkbox to see more information about the add-on. The documentation button leads to the main page on this site.
Blender has automatically unzipped the repository to the place where it looks for add-ons.
The advantage of this method is that it should work on all operating systems. Alternatively, you can unzip the archive manually and make a link from the add-ons folder. This enables you to refer to a single copy of the add-on from several versions of Blender, but requires more manual work.
Once the add-on has been installed, you will find it under the Import-Export category. You may have to restart Blender to see anything here.
When the add-on has been installed, you should check the paths to the DAZ libraries. They are found in the Settings panel in the DAZ Runtime tab, which is located in the Tools shelf (to the left of the viewport) in Blender 2.7x and in the UI shelf (to the right of the viewport) in Blender 2.8x.
A .duf file saved in DAZ Studio does not contain the actual data in the way that Wavefront object or Collada files do. Instead it contains links to various asset files in the DAZ libraries, and these assets can link to other asset files as well. In order to find the assets, the DAZ importer needs to know where the DAZ libraries are located. Up to three different library locations are supported, but a default installation of DAZ Studio only uses two.
The DAZ importer makes a guess which works on my computers, but they all run on Windows 7 and the paths may need to be changed on other operating systems. However, the changes only need to be made once. When you have changed the DAZ paths, press the Save Default Settings button to make the importer remember your settings. The next time Blender starts, the new library paths are used.
The settings are saved in the file "~/import-daz-settings-27x.txt" (Blender 2.7x) or "~/import-daz-settings-28x.txt" (Blender 2.8x). Here "~" is your home directory. You should have both read and write access to this file under all operating systems.
For an example of what can go wrong with the DAZ paths, and how to fix the problems, see this blog post.