It uses freight cars, which are ordered in the railyard (in the top right of your city screen). Each car's construction requires two labor units and one unit each of coal and steel. Cars once built run for ever with no maintenance or repair costs.
Available items, if in surplus, are assigned to freight cars using the first item ("Give Transport Orders") on the main menu to reach a screen where sliders determine which items are carried in a particular turn.
There is mention of barges but no practical application of them (by contrast with Imperialism 2, where goods that do not come to the capital by road/rail, including almost all fish, require merchant marine transport).
Quoting from the readme file for v 1.1:
took to create that unit. When performing a landing, the allowed size of a landing force is equal to the total number of arms it took to build all the ships performing the beachhead operation. For example, a frigate cost two arms to build, so a landing force composed of four frigates allows a force of size eight. This could be eight regulars (one arms each), four artillery (two arms each), or some combination of the two. This number is also used when deploying troops farther to distant provinces; the force size that can be moved in one turn is equal to one fifth of your internal transport capacity (built in the railyard).
A General counts as 1 (?).