You could arrive in Fremantle via cargo ship or cruise liner. That way, you would, after a long journey, arrive at a long flat sandy coastline dotted with trees and make for the obvious port.
By car Take Leach Highway west, Stirling Highway south-west or Canning Highway west. From the south, take Rockingham Road. From the north coast, West Coast Highway and the Curtin Avenue lead to the port. From Perth city, Fremantle is about a 30 minute drive.
There are many TransPerth buses that arrive and leave Fremantle. Routes 98 clockwise and 99 anti-clockwise are quick and frequent services that lead to Fremantle. They terminate at the Fremantle Railway Station.
Frequent commuter trains from Perth leave from Perth's City Station, and makes the 25 minute trip to Fremantle via Perth's western suburbs, culminating in a breath-taking view of beach, ocean and port before arriving at Fremantle station.
See the TransPerth Journey Planner (http://www.transperth.wa....) for more info on trains and buses.