Hmm...that sort of barrel is going to be useful only for "cask conditioned" type beer. A couple of options with it:
1. Ferment beer to completion. Add to barrel with some priming sugar and seal. Wait another week or two. The beer will now be carbonated, and will be more likely to stay that way if you manage to chill the barrel. However, as you pour the beer, relieving the pressure, it will go flatter. That's pretty much exactly how cask-condition ales poured with a beer engine work.
2. If it can have a CO2 tank connected to it, you could put 10PSI on it, chill it, and wait a good long time for it to carbonate. Once it is carbonated, reduce the CO2 pressure to, say, 2 or 3 PSI to dispense. The pressure that the CO2 keeps on it will keep the beer carbonated. But I doubt your barrel can connect to gas, if it's what I'm thinking of.
We use cornelius kegs. When carbonating, we crank the gas to 40 PSI or so. If the beer is chilled and you shake the keg, it can be carbonated in minutes. In order to get a really bubbly beer, you probably have to switch to a gas-pushed setup or bottle your beer.
Good luck!
Janx