Your arrival in Pirate’s Atoll, whether by hypergrid or cruise ship, will disembark at the New Tortuga Station. From there you can continue on to other destinations on the hypergrid or choose local destinations within the Atoll. Atoll local trains are at the West end of the station. Click on the teleporter and choose a destination, then click the teleporter again to go there.. Train (teleport) stations can be found throughout the islands. Just look for the AToll Transportation Authority teleporter, and use it to go to a new destination.
Most of Pirate’s Atoll is reachable by walking (or flying) as all of the islands are connected by bridges. You can also rez a self-serve water taxi on many of the islands, by ringing the bell on the dock or on the beach.