Gas bottling credit: Adrian Mann
The purpose of a Jupiter Orbital Mining Platform, or JOMP, would be to collect and "bottle" hydrogen gas from Jupiter's atmosphere for shipment to Venus, where it would be used in the terraforming process.
As a secondary purpose, the platform could extract and "bottle" Deuterium and Helium-3 for shipment to Earth, where it could be used in our fusion reactors if they ever reach the break-even point. However, this may not be economical because it would be cheaper to mine and ship Helium-3 from the Moon, and to a lesser extent, Mercury, to Earth. Deuterium can be extracted from seawater.
Nevertheless, extracting and bottling fuel for fusion reactors from Jupiter may not be altogether useless. This fuel may be a vital resource for any colonies in the Outer Solar System, or the mining platform could serve as a waystation of sorts where ships making their way out of the solar system could refuel or stock up on extra fuel for their fusion reactors.
The mining platform itself would be in low orbit around Jupiter and a long tube, tower, or hose would extend down from the platform into the upper level of Jupiter's atmosphere. An air pump or maybe even a giant vacuum cleaner would siphon gas from Jupiter's atmosphere and pump it into a container like a tank, capsule, or possibly a giant balloon. Once filled, the container would be sealed and then either moved to a storage room or sent along a conveyor belt to a mass driver. The entire platform would best be automated.
The reason I say EITHER is because I'm not sure you could safely shoot a container of hydrogen gas through the asteroid belt and past the inner two planets and hit Venus with it. In fact, I'm almost willing to say it's unlikely. Besides, you can't always see Venus from Jupiter.
The containers would most likely have to be transported the old-fashioned way. This sucks though, because you have to have fuel for the transport, and either a person to navigate through the asteroid belt, or a REALLY smart AI to navigate through the asteroid belt. Fuel is EXPENSIVE, and that AI would be hard to program. And it would suck really bad to have to have someone manually pilot the transport (since laggy remote control would be too dangerous), since you have to feed him, and have exercise thingamajiggies on the ship to minimize bone calcium loss because of zero gravity.
As for the containers themselves, they should be sort of thin. This will make them cheaper and they will dissolve more easily in Venus' sulfuric acid atmosphere.
The platform could be powered by either solar cells like the space station, solar wind, a fission reactor, or a fusion reactor (if we can ever make them economical). The nicest advantage of the fusion reactor is that the fuel could be produced right on the platform.