There are few things you should remember when you’re using SQL in WordPress. The most important, I guess, would be table prefix.
So your query should look something like this:
global $wpdb;
$sql = "SELECT kategorie.id, ogloszenia.kategoria, klient_id ".
"FROM {$wpdb->prefix}category kategorie ".
"JOIN {$wpdb->prefix}ogloszenia_kupione ogloszenia ON (ogloszenia.id = kategorie.id)";
$results = $wpdb->get_results( $sql );