You can arrive in Fethiye by bus from Antalya or Dalaman. Both cities have airports. When you arrive in Fethiye, you can also visit Kayakoy ancient city, and the Amyntas tombs which are also located right in Fethiye.
To proceed to the trail, you need to take a local bus from Fethiye to Oludeniz. You can tell the driver ''Lykia yolu'' and they will stop the bus at the closest place to the trail, even if there is no bus stop. You need to get to
this place, this is where the sign is.
You can also visit Oludeniz beach and start hiking from there, but in that case, you will miss that Lycian Way arch.