Taran is tasked with escorting Princess Eilonwy to the Isle of Mona, where she'll be taken in by distant relatives -- the king and queen, who will help her learn how to be a proper young lady (an idea she finds ridiculous). They sail there on a ship "captained" by the island's Prince Rhun.
Once they reach the island, Taran runs into Fflewddur Fflam, who's enjoying barding again -- even if the castle's steward, Magg, has an intense dislike of his music. Shortly after that, Taran discovers there's a threat to Eilonwy in the castle and tries to save her from it without letting her know she's in danger. That goes poorly and he joins the rescue effort instead (also led by Rhun -- or at least Rhun thinks so).
The companions also meet the world's littlest giant (why does that sound like it belongs more in The Phantom Tollbooth than here?) and a mountain cat that we'll get to spend a lot of time with. There's a lot of links to the first book as well as the last book in the series here.
The introduction by Alexander was great -- I wish I could hear more of his own takes on the books. Langton was solid. Again, I think he could talk a little faster -- but that's minor. His Prince Rhun's "Hullo"s are just what I've heard in my head all these decades.
This is probably the most entertaining of the lot -- there's some really good comedy here. Taran grows up a lot more here than he does in other books, I think, which adds something more than just entertainment to this book. It's possible that this is the one in the series I read the most as a kid. The story isn't as rich as I remember, but factoring in the growth in characters and the entertainment factor, the experience as a whole was pretty satisfying -- and I'll take that.