It's pretty usual ARPG fare with attacks of various strength (augmented with having different weapons, with different speed, stagger, strength abilities), and your dodge, roll n counter attack stuff. The additions to these are the warping, which lets you warp sort of out of battle to recover, and warp in causing extra damage, you can (on bigger creatures) target specific points, allowing you to, for example, lop off horns or limbs or what not. You can also command your party to do certain actions and also link with them for certain attacks too.
The magic acts more like grenades, with a bit of Rikkus "mix" stuff in that you craft your magic spells before hand fusing several elements and able to use items to so potions would help create a spell that heals your guys while setting enemies on fire. There's other magic available too through the Ring of Lucii but that's sort of end-game stuff (they've shown off "Death" for example).
There's also the summons, but not much is known on how those will work in combat. While Ramuh shows up in the Duscae demo if you hit 0HP it's guessed that won't always be the case n they'll be much more special n limited than in prior games.