Graphics - About as good as they're going to get with the DS' hardware limitations. I think the average framerate is slightly lower than FF3, but that's probably due to the fact that you have up to five party members and six monsters on screen in a battle. Still, the graphics really shine during the cut scenes, where the characters can move in any fashion as the story dictates. Battle animations have been given neat little touch-ups, such as the critical hits being a different physical maneuver than a normal strike.
Sound - Brilliant. Absolutely brilliant. The entire score has been re-recorded and sounds better than it did on the SNES. The noise of the spells are mainly the same (Bio, anyone?), but updated. Finally, the voice acting during the cut scenes varies from meh to excellent. Frankly, the mere fact that there's voice acting in this game is damn cool.
Gameplay - Well, what can one say? It's familiar FF stuff. I will say that the ATB system has been implemented well, with distinct turn and action gauges. One of the coolest additions is augments, which allow your characters to learn new abilities (or abilities of other characters which have left your party).
For example, you can obtain Palom and Porom's Twincast ability, and equipped on the right characters, can unleash the most powerful spell in the game. In that vein, most of the secondary characters have been given extra abilities not present in the SNES game. Rosa can Pray, which allows everyone in the party to recover both MP and HP. Cecil (as a Dark Knight) can invoke the Darkness ability, which allows him to double his damage at the cost of some health. Tellah can attempt to recall one of forgotten spells in battle.
As a final gameplay note, Edward still sucks, just not as badly as before.

In all, it's game we should've gotten originally. There's more dialogue, better graphics, cut scenes with voiceovers, and new features. I'm guessing that if you're an obsessive bugger like I am, I'd say you're looking at around seventy hours' gameplay to completely finish it out completely. For $40 USD, that's a pretty cost-effective choice of entertainment.