You need to use Space Yard ships to create enough Starbases in the same sector as a star to hold the 100k of plating, the 100k of cabling, and the Ringworld generation component. When all of them (11 separate bases) are completed, you can use the Stellar Manipulation icon which'll appear when you select the base with the Ringworld generator on it.
As for the expense, it depends quite a bit on the nature of your game. The smaller the map, the more likely you'll need the room enough for it to be worth the cost.
Of course, they're cool on any size map.
Re: Ring Worlds
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