How to use og_is_member() API?
I'm not sure what difficulty you're having using the function or what Drupal version you're on, but according to drupalize.me, in Drupal 7 og_is_member() takes parameters $gid (ID of group), $entity_type (defaults to 'user'), $entity (defaults to current user), and $states (optional, defaults to all), and returns TRUE if the entity (e.g. current user by default) belongs to the group.

For example, to find out if the current user is a member of group 4, I would use something like,

$current_user = global $user;
if (og_is_member(4, 'user', $current_user)) {
  // show the user some stuff from group 4
}


The above code is not tested but should get you started.