This combo is actually fairly straightforward. Círdan the Shipwright and Arwen Undómiel discard allies, Caldara discards herself, free allies enter play, Fortune or Fate brings her back. The details can be tricky, because there's a lot going on here.
As soon as Caldara dies, Prince Imrahil becomes a hero if he is in play. This doesn't help on the turn that she returns him from the discards, but in future turns this brings you three allies instead of two. For that reason, it's often worth playing him for resources. Sword-thain gives a fourth hero, ideally on Elfhelm or Lindir, but Háma is fine too. Glorfindel sometimes dies blocking, and Emery dies frequently, but it's better to Sword-thain as early as possible even if they are the only targets.
Card draw is very flexible here, with the usual combo of Imladris Stargazer with Zigil Miner, plus the card draw that Player 1 should be sharing occasionally. Zigil Miner can hit Hidden Cache, Ered Luin Miner, Elven-light, and any allies you need to ready for Caldara. Questing is accomplished mostly by Pelargir Shipwright, Northern Tracker, Arwen Undómiel and sometimes Círdan the Shipwright. However, Narya is incredibly powerful in this deck, having options for extra attacks, blocks, healing, and/or card draw.
In the late game, once this deck runs out, we have some incredible combos involving Dwarven Tomb and Map of Earnil. By using one on the other, and then the other on the first one, an extra Dwarven Tomb is added to the bottom of the deck. Each cycle of this combo earns us an extra play of any Spirit card. A Test of Will is the classic of course, and Fortune or Fate can be useful, but by then usually all allies are in play. Instead, we have Stand and Fight and a Gandalf from Player 1, which we can do once every turn pretty easily, given 4 heroes and money from Denethor and Arwen Undómiel.
The Caldara deck is getting awesome. I've been playing this basic deck with Beregond instead of Cirdan, but Cirdan is perfect with all hose big allies! Nice work!