I grabbed a copy of the episode and started making notes. The Dyson Sphere in that episode was a hollow shell of carbon-neutronium 200 million kilometres in diametre, enclosing an unstable G type star. The only way in (or out!) was through a giant portal which pulled the Enterprise in with massive tractor beams. Best of all, the Enterprise had very little time to do any exploration of the Sphere's interior, so pretty much everything else was open to development by me and my devious little mind (cue sound effects: crash of thunder outside window, mysterious organ music and maniacal laugh)! At the end of the episode, Scotty went off in a loaner shuttlecraft, the Enterprise continued on with its mission, and Star Fleet Command assigned two Science vessels to explore the Sphere.
That was season 6 of TNG, stardate 46125.3, or the year AD2369 (depending on your preference). Since that time, the Federation has seen the beginning of exploration of the Gamma Quadrant (2369 through 2372), contact with the Dominion (late 2370), an attempted coup by Star Fleet Admiral Leyton (2372), war with the Klingon Empire (2372 - 2373), a Borg attack on Earth (2373) and all-out war with the Dominion and Cardassia (2373-2375). All these events have contrived to draw Star Fleet's attention away from exploration of the Dyson Sphere. All that is currently devoted to the mission is a skeleton force consisting of a small ground base, a single "duck blind" outpost and a number of small craft. The start of the campaign was set at stardate 52495, in mid-year AD2375. The current date in the game is 52955, toward the end of AD2375, just before the end of the Dominion War.
Within the Dyson Sphere, the PC's are cut off from the vast resources of the Federation and Starfleet. They cannot have a platoon of Security NPC's show up at the tap of a Commbadge. They are not completely isolated as in Star Trek: Voyager, but they are in a situation where they must handle things themselves. On the other hand, they do have some support in the form of Dyson Base and the other five runabouts. There is a monthly visit from Starfleet, which will allow new PC's to arrive to replace dead, injured or just plain boring characters, and will also allow for technology upgrades, news from home and some interaction with the outside universe.
Dyson Base is positioned on Freeman's Island in a large body of water near one of ten portals into the Sphere. It has just been upgraded and currently has a complement of 21 officers, NCOs and ratings, including 6 ground forces personnel. Each of the six Danube Class Runabouts has a crew of four. In addition to the runabouts, Dyson Base is equipped with four Type 7 Shuttlecraft and two Peregrine Class Light Attack Craft. There are a total of 48 Star Fleet personnel stationed in the Sphere, including the crews of Duck Blind One.
Duck Blind One, a concealed outpost observing a small village of sapient humanoids called the H'Ranna to the west of Freeman's Island, has a crew of one officer and three enlisted personnel.
The base is equipped to monitor sensors placed by the runabouts, analyse data collected by these sensors and the runabouts, and maintain all its equipment and vehicles. There is a vehicle maintenance bay capable of swapping the mission specific modules of the runabouts and servicing them and the shuttlecraft. There is a small hologymnasium module for recreational purposes and a sickbay equipped with a Emergency Medical Holographic Doctor. Food is provided by replicator.