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.
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.
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.
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.
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.
For an example of what can go wrong with the DAZ paths, and how to fix the problems, see this blog post.