In the Population and Production window (first icon of the System Map view), go to the Civilians / Ind Status tab of any given colony. There you can setup contracts for the colony to supply/demand X units of certain installations, selectable from the drop-down menu. Once you establish a supply contract in one colony and a reciprocal demand contract in another, the civilian shipping companies will take care of transporting the items.
Be advised, for a colony to actually supply the facilities you're asking, it has to have them built there. Unlike civilian vessels, they won't appear out of thin air to fulfill the contract.