He was born in Lochovice in Bohemia and began his musical career there as an oboist in the service of Countess Valpruga Netolická.

He was an oboist for archbishop Hieronymus von Colloredo's orchestra and played violin and violoncello in Salzburg State Theatre.

In 1785 Fiala moved to Vienna, where he served as a horn player for Nikolaus II, Prince Esterházy, and in 1786 to Saint Petersburg where he worked in the court of Catherine the Great.

Finally in 1792 he became Kapellmeister, cellist and composer for Joseph Maria, Prince of Fürstenberg in Donaueschingen, where he spent the rest of his life.

During Fiala's tenure in the court of Friedrich Wilhelm II, the king honored Josef by giving him his own family crest.