I am familiar with the plastic pressure barrels, I have two.
Carbonation is the same as bottling, get the sugar and the beer into the barrel and close it up for three weeks. It will generate it's own gas to a point where the pressure relief valve will let some go. This will be enough gas to serve most of the beer, when the pressure gets low , you simple connect the gas cylinder and give it a couple of seconds , that gives enough gas to keep serving, it may need several charges of gas as you work your way through the second half of the barrel. Of course this is all dependent on the particular brew , weather , the rate of use, temp etc. I have only had one brew that served to the end without needing a gas top up. They work , but nothing like a corny ( which I haven't got).