The best way would be a taxi but you can take a bus also. Ephesus is aprox 17 km from Kusadasi and it will take you 20-40 minutes to get there.

Catch the Selcuk minibus- leaves about every half-hour or so and ask for Ephesus (most people on the bus will be going to Efes)- about $5 one way.

Here is a map of Kusadasi with the towns bus station marked.

http://www.kusadasi.com/images/minibus.gif

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