So what exactly did they do? The set (the ship's bridge) and costumes were pure TNG, with Trek characters "cast" as the Pinafore ones in appropriate roles, often by performers physically resembling the Trek actors. (However, if your Geordi is pasty-white, you're just not trying.) For instance, the young lovers Josephine and Ralph were done as Counselor Troi and Commander Riker. (She: excellent. He: dreadful.) Dick Deadeye was Worf. I need hardly say who the Captain was. The most successful matchup, and the best acting performance in the show, was Sir Joseph Porter as Admiral Kirk. As the director's note observed, "The similarities in personality between the two made this an easy choice." Gerar Mazarakis, who played the part, had a witty and plausible knack for a parody of Shatneresque overacting. It made for a Sir Joseph utterly dissimilar in tone from any I'd ever seen before, but surprisingly effective.
The show was consequently packed with innumerable clever bits of stage business that any Trekfan would get a kick out of. For instance, Little Buttercup (Lwaxana Troi) was selling from her basket, among other things, tribbles (of course), and those tribbles made an unexpected reappearance in quantity later on in the show, of course.
The lyrics and dialogue, however, were almost totally untouched. No attempt was made to reframe this story of 19th century British class roles or to update the ancient nautical dialogue, or change the names, or address inevitable oddities resulting from the "casting," like Deanna being Picard's daughter.
Just a few changes were made, mostly in the spoken dialogue. Sir Joseph is beamed on board, yes, but from his barge (it's still a barge). There were just a couple minor, and one major, changes in lyrics. The major one was in "For He Is An Englishman":
For he might have been a VulcanBut in spite of all temptations to belong to other nations, he remains an Englishman, not a human or a citizen of the Federation or anything like that.
A Trill, or Q, or Romulan
Or perhaps Cardassian
As a G&S production, it was basic for this group, which is sometimes better than this. Josephine (Christina Krawec: give her namecheck credit), as I mentioned, was excellent. Most were not, though there were a few honorable exceptions. Most impressive of the exceptions was a fine performance of the unaccompanied madrigal "A British tar." Just imagine watching it being done by Riker, Data, and Geordi LaForge.