Get the tarball or the zip file of the module from Drupal.org (MobileKey on Drupal).
Go to one of you module folders and extract the file you downloaded.
The default installation folder is sites/all/modules, if you have a multi-site installation and want the module for just a few sites, go to sites/<sitename>/modules instead (create the modules folder if it doesn't exist yet.) It is recommended that you do not install under the top modules folder as this one is reserved for Drupal Core modules.
At that point, go to your Drupal website and go to Administer » Site building » Modules. In the Mobile field set, select the MobileKey module and click Save.
Note that the ThemeKey module is required and must also be installed. If you cannot select the MobileKey module, that's because the ThemeKey module is not yet available in your installation. Otherwise, if the ThemeKey module was not yet installed, clicking on Save will first ask you whether you'd like to do so and then the installation will proceed with the ModuleKey module.
Now the module is installed. Note that it will have no effect until you apply settings as shown in this documentation.