Explain how religions use works of art to encourage and spread their beliefs.

Cool question. Originally, art was used to promote religious ideas among the illiterate peasants - it's easier to understand a drawing over a book, right?
Probably the best example of art to promote religion has to do with the Baroque era of art - guys like Martin Luther and Jan Hus criticized the practices and power of the Catholic Church, and many people turned to Catholicism. So the Church began commissioning people like Caravaggio to paint religious subject matter in a way that was accessible to the common man. For example, in 'The Calling of St Matthew', Matthew is depicted as a slightly drunk guy in a tavern and Jesus was just some random dude. By making these religious figures lower, people empathized with the religion. Just an example.