After installing any module I get "The website encountered an unexpected error. Please try again later."
Enable error reporting in Drupal. This way, Drupal can print the errors and stack traces on the page when the errors occur. Also, consider enabling the module using Drush particularly with --verbose and --debug options. This prints logging info while enabling the module.

The source of this could be anything. It could be a bad module install script, bad configuration, bad module hook code, or a malformed template (for that page). I usually get these pages when code tries to access non-existent properties or indexes or have modules that don't play nice with each other. This usually look harmless. But if the error cuts into execution and there was data that was still to be saved, it might result in a bad system.