Kiama is on the South Coast City Rail line. Timetables for the train are available on the City Rail page and typically take around 2.5 hours. The train journey is one of the most spectacular routes in Sydney and goes through the Royal National Park and along the cliff edges with great views of the Pacific Ocean (sit on the left handside of the train!). Track work takes place on some weekends and a replacement bus will be used instead of the train. This can be checked at the City Rail trackwork page.
Kiama can also be accessed by car. The journey from Sydney airport is approximately two hours using the most direct route.
View Larger Map
With a little more time you could drive on the Grand Pacific Drive which takes you through the Royal National Park (mind the kangaroos), past wildlife parks, a brewery, wineries and large Hindu and Buddhist temples.
The Premier Motor Service also provides a coach link between Sydney and Kiama.