There are a number of public and private transport companies which service Willoughby. To plan a trip using public transport, the Transport Info website will help you. Just put in where you are, where you want to be and when, and it will tell you how to get there.
There are three train stations in the Willoughby area; Chatswood, Artarmon and St Leonards, which are all on the North Shore Line. Sydney Trains provide regular services to and from the Sydney CBD both day and night, which is often cheaper and more convenient than driving.
Public bus company Sydney Buses, and private companies such as Transdev and Forest Coach Lines. Visit their websites for contact information and routes.