The stories online are often made a little fluffier. I'm just going to give you the facts.
In early 1883, a girl named Fortuna Agrelli fell ill in Italy. She was sick (almost near death) for a little over a year. The doctors had given up and as such, the family began a series of Novenas on 16 February 1884. About two weeks later on 3 March 1884, Our Lady of Pompeii appeared before Fortuna and instructed her on how to pray the 54 Day Rosary Novena.
Our Lady was seated on a high thrown, with the Divine Child on Her lap and a Rosary in Her hand. They were surrounded by luminous figures and dressed in golden garments. Sts Dominic and Catherine of Siena accompanied them.
Just so we're clear, a Novena means to pray the Rosary 9 days in a row. The 54 Day Rosary Novena is in essence 6 Novenas prayed in a row. The first 3 Novenas (27 days) are said in petition and the remaining 3 Novenas (27 days) are said in thanksgiving (whether or not you received your request).