To build a Cableway, select in in a shop and then place on a free slot of the first island (from which the resources will be streaming). Approve the purchase. Then the button with the red exclamation mark (!) will appear, meaning that the Cableway is not connected. Press this button to select a cableway. Then drag the connection button to another available slot on another island.
The cableway will start working. It's possible to upgrade it to increase the quantity of resources transported.