Your table should be configured using ENGINE = MyISAM (not InnoDB), and the columns you are looking for should be set to FULLTEXT.
You can easily set the table in MyISAM in phpMyAdmin through the "SQL" tab ...
ALTER TABLE `tablename` ENGINE=MYISAM;
In Joomla 2.5+ (probably 3+ as well) in my request as a where clause, which I used ...
->where('MATCH ('.$db->quoteName('columnname').') AGAINST ('.$db->quote($words_or_phrase_to_search_for).')');
Further testing is fine, but so far it is working as expected.
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