$db = JFactory::getDbo();
$query = $db->getQuery(true)
->select('user.firstname, user.lastname, leadership.leadname, leadership.lead_des')
->from('CLUB,LEADERSHIP,USER')
->where('CLUB.CLUB_ID=11')
->where('LEADERSHIP.USER_ID=USER.USER_ID')
->where('CLUB.CLUB_ID=Leadership.CLUB_ID');
Multiple where clauses by default clubbed with AND. You can give the glue (AND or OR) explicitly as second option to the where function above however it is optional. Quote from Joomla API docs for JDatabaseQuery->where function:
string $glue - The glue by which to join the conditions. Defaults to
AND. Note that the glue is set on first use and cannot be changed.
Or the alternative is you can manually combine in single where clause. You can use this method to mix OR and AND in the where clauses in a complex query.
$query = $db->getQuery(true)
->select('user.firstname, user.lastname, leadership.leadname, leadership.lead_des')
->from('CLUB,LEADERSHIP,USER')
->where('CLUB.CLUB_ID=11 AND LEADERSHIP.USER_ID=USER.USER_ID AND CLUB.CLUB_ID=Leadership.CLUB_ID');