My lords...
About Dyson Spheres and all that...
I have done some theoretical work for another (to date unreleased) Sci Fi project that deals with the concepts you all have touched on here.
In the afformentioned background, certain species (lets call them "Species X") have the level of technology neccessary to produce such structures. The main line of reasoning behind their construction is in answer to a growing population problem.
In this yet to be seen project, the line between biological and technological life is so blurred, that virtual immortality is available to almost every citizen through advanced medical procedures. The only downside is, there is no known means of 100% effective contraception, as there are psychic factors at work, as well as physiological ones. It boils down to a society that has almost no negative population growth, but plenty of positive.
To combat this problem, Species X long ago came upon what is known amoung them as the "order of settlement" a logical progression of star system development. It is a program designed to run over hundreds of years (people tend to reckon time differently when live live for a long, long time) and with predictable results.
Step 1:
A star system is selected to be developed, provided that it meets certain criteria, namely, A single, relatively stable, young to average age star, with billions of years left to it, and of average mass. (too large a star and the "Orbital Environment" would be too large to be cost effective.) an uninhabited system is preferrable.
Step 2:
A stellar orbit is selected in the "best" part of a star's habitable zone. Several large "Service Satellites" are deployed into the selected orbit, serving as little more than huge construction platforms and facilities for workers. It is also at this step that organic samples are taken from surrounding worlds for "Genetic Tailoring" to fit them into the final Ecosystem. Raw materials needed for construction are also prospected and processed at this time.
Step 3
Over the next 50-75 years, most of the star system's raw materials are converted into forms used in construction. The Service Satellites are connected into a superstructure along the perimeter of the orbit. By the end of this time period, the "ring" in "ringworld" starts to take shape.
Step 4
The next 50 or so years are spent plating up the superstructure, providing a good basic foundation for the Ecosystem to take hold. Gas from Gas Giants is refined and processed to form the desired atmosphere for the ringworld. Kilometers tall "gravitic stabilizer" towers are installed on the edges of the ring. These exert a subtle, self maintaining force of gravity keeping the ring stable, as well as keeping it at a steady rotation. It is also during step four that temporary "artificial night" plates are put into orbit above the Ring, getting the new ecology used to a regular day/night cycle.
Step 5
Now that the ring is done, the next 50-100 years are spent processing the star system's remaining raw materials and locating / importing more raw materials from a (hopefully) nearby system(s) It is when these sources of materials are secured that the expansion of the ring environment begins. The edges of the ring are built up with more massive superstructure, and the Sphere starts to take form around the star, with the already established Ring as its equator.
Step 6
The Final phase is a busy one. The next 100 or so years of construction, the rest of the spherical superstructure is plated up (no small task) and the ecology is expanded/transplanted everywhere around the sphere. Prefabricated buildings and other structures are added to the sphere's interior surface, and a permanent "artificial night" is put into place. No problem.
The above exposition assumes a technological development far and away from what is seen in Traveller, but it gives some sort of thematic idea as to what would be involved in the construction of so fantastic a thing. It assumes that some form of matter rearangement can be done, to convert raw materials and gasses, as well as superadvanced automated systems geared to work on a near unimagineable scale. It establishes an idea of both the Ringworld and Dyson Sphere as stages in a mother of a construction project...
"The Home Depot" in that part of space must be very impressive indeed...
(Bows) By your leave, Lords...