Robin is a truly a difficult character to dissect... Perfect to take a crack at.
Starting with specials, lightning spells seem to be the neutral. I'm assuming that you have a sort of charge meter (without a visible meter of course) in which, when you have a full meter, you perform Arcthunder, after which your meter empties and any subsequent use will be a measly Thunder. For as long as you don't use the attack, the meter will charge back up, with Elthunder being the attack used at half charge. Think of it like the Wario Waft, except with an extremely shorter charge time, presumably. Thoron would be a regular charge attack you would perform by holding the button, and can be done at any time. What I'm unsure of is how the book gets used up, though I assume it just happens if you spam the attack too much, which would leave you without the use of the attack at all with a slightly lengthened time until the meter charges back up and the book returns. Though that's just a guess.
Fire would be the side special with the same mechanic, Arcfire at full charge, Elfire at half, regular Fire at low, spamming loses the book, and you can charge it for the strongest fire attack (I'm not sure what fire spell would be the equivalent of Thoron in Awakening).
The recovery is where things get really tricky, would they actually make a recovery move be limited like this? I believe so, considering the footage in the trailer, and I've got just the idea of how this might work. It's unclear if he goes into a helpless animation as he does go off-screen, but from how it appeared to be used twice in quick succession, I believe this to be a multi-use recovery. Of course the charging mechanic stops this from being the most OP recovery in history, as when you have no book, you would likely end up in an instant helpless fall with no boost whatsoever. That would make this a move you wouldn't want to use just for attacking, rather you would want to keep a full charge so you can Arcwind > Elwind > and Wind back to the stage. You would presumably be able to charge it as well, resulting in a super high boost, but it would leave you helpless as opposed to using it regularly.
Nosferatu appears to be the odd sheep, though that's common of down specials. As Nosferatu doesn't really have any lower forms in Awakening, it'll probably be just a single kind of attack with a single function and no separate charge levels, though spamming it would still make you lose the book. As Nosferatu is a life leaching attack, which appears to be faithfully recreated here, it's a bit of a different take on Ness and Lucas' Magnet, in that you likely have to 'trap' the enemy as you would need to do for a counter, rather than absorbing any projectiles. Of course, it's unclear just how much this damages/heals at this point.
The swords are also quite confusing, some are saying that the regular combo/tilts use the bronze sword, while the Levin sword is used for smash attacks, so I'll just go with that since I have nothing better. The confusing part is the apparent aerial smash attacks, which as mentioned before will likely function as Samus' missiles/super missiles, though I would assume that the right stick will still function as a quick smash (that'll really mess with me as well...) The Levin sword would also disappear if you spam smashes too much, but would appear after a set amount of time. That's all I can gather so far.
Of course the easiest part of his moveset to analyze is his final smash which was blatantly spelled out in the video. He just summons Chrom in his swimsuit to knock out everyone else (for various different reasons).