How to get current logged-in user details in multisite?

As described in the documentation, you have call this inside a hook.

For wordpress versions < 3.4: use the init or any subsequent action to call this function. Calling it outside of an action can lead to troubles. See #14024 for details.

Example:

add_action('init', 'get_user_email');
function get_user_email() {
  $logged_in_user = wp_get_current_user();

  if($logged_in_user->ID != 0){
    $email = $logged_in_user->user_email;
  }
}