This feature is not available until the player has 1500 Vassals on Newport.
You will need to upgrade the harbourmaster to level 2 which is done by clicking on the harbourmaster and fulfilling the requirements as outlined in the sold green arrow to the left with a mouse over move.
The pre-existing pier that extends from the harbourmaster into the water then needs to be capped with the “dock” which is a construction item in the Infrastructure group in the vassals’ subgroup. The dock is not a dock at all in the true sense since it is really the "transport storehouse" in this game. The translation to English from German is not as good as it could be, in my opinion. Any island you colonize will "convert" the colonizing ship into a harbourmaster complete with the “dock” for all intents and purposes, so that end of the cycle is already ready to handle transport.
You must also build at least one transport ship via the shipyard with parts that you made in the naval engineer. Always activate ships while viewing Newport which simplifies ship management when it comes time to abandon another island.
You set up a transport route in the Island Overview menu with the Routes tab that looks like 4 crates. Click on the + button to add a route. You then first double click the start island and then double click the destination island. You will then be presented with a list of available ships to transport which will later include trade ships that also can transport goods but at a slightly slower speed (also with an added upkeep cost and captain cost).
Double click on the available ship and you will be shown the warehouse menu of materials for the start island where you select what you want to send to the other island. Then click the next button to take you to the destination island.
If there is still ship capacity available, you may select what is left for return to the start island from the destination island. Click next and you will be presented with a summary page where you can optionally name the route and select continuous if you want the ship to do an endless loop between the two islands that can be stopped at any time by you by clicking the x button in routes later. The ship must continue its loop until it completes the current one.
Ship capacity is total for both directions so do not attempt to ship 40 to the destination island return with 40 to the start island (assuming a ship capacity of 40). You could split the shipment to be 20/20, 30/10, 35/5 but the sum of both directions must add up to no more than total capacity.
You can use the route name to help define trips duty which makes dealing with multiple cargos much simpler. I use something like paper110n+++z which lets me know that this ship is shipping paper, has a capacity of 110 and is going from Newport to an island starting with the letter “z”. The 3 plus signs are a code that lets me quickly locate routes that are continuous but that I want to cut off after a number of hours (or at least review the transport progress by checking the destination island for paper inventory). More + signs just denote that I should cut it off sooner than others.
Continuous routes cannot be viewed for current progress while active.
I use the default "My Route" strictly for single loop transports.