The installation process of this module is very easy, you just download the suitable version for your Drupal core version, and enable it (How to Install a module in Drupal 7).
The Blizzard Community Platform API 7.x requires the Entity Module. The 8.x version does not need this dependency as Entity Module is part of Drupal 8.x core.
After enabling Blizzard Community Platform API, go to your configuration pages (admin/config) and enter World of Warcraft > General Settings. Alternatively, you can click on the configure link on the modules page.
In the configuration pages, you can set your regional settings, the default locale, and your private API key. Note that the base module does not make use of the default regional settings but developers that build upon this library may require this settings so it is considered as good practise to check them.
WoW Data Services
Enabling the wow base module will grant you access to the WoW Data Services, sort of daemons that periodically fetch data resources for a given region and language. You can have more information on implementation in the developer documentation.