The mechanics are very simple and very old-fashioned. You decide all of your characters attacks/whatever at the start of the round, and then then round plays out. Unlike older game though, this game is (usually) very finely tuned. Enemies throughout the game provide a consistent challenge, but not are not overwhelmingly difficult (as long as you plan your rounds intelligently). This turns the relatively simple battle mechanics into genuine strategy because the choices you make actually matter; there isn't usually a best-for-all situations attack setup. Unlike final fantasy games, you won't just be pressing the X-button a bunch to get you through the random encounters.
The game does have some nagging old-school mechanics that weren't finely tuned though. The aforementioned random encounters are *extremely* frequent; get ready to fight a lot. Combine this with random encounters that aren't pushovers, and its hard to play this game in less than 2-hour chunks and expect to make progress (unless you're just running through a city and managing gear/inventory).
Additionally, it has the old JRPG standby of enemies having numerous attacks (some very weak, some very powerful) that they perform at random. This means the same battle can be very easy or very very hard depending on whether they do a sort of average of their moves, or if they hammer you with multiple "power" attacks. This rarely happens with random encounters, but is a big problem with boss enemies. There have been multiple bosses that wiped my entire party out from full health to dead without me getting a turn in between.
Fortunately, death is not a game-over in this game; you go back to the last place you saved and have everything you've accumulated so far (items, xp, etc) except your gold total is halved. Early in the game you're so broke from buying items its not a big penalty, and later in the game you can find banks to store your excess cash and protect it from this (you have to go and withdraw the money before you can use it though).
Also, its not possible to play this game without noting on how beautiful the graphics are for the PS2. Even after being used to HD graphics, this game still looks great for what it is. I'm usually not a fan of the artist's style (Dragon Ball Z), but I can't deny that the art direction in this game is top notch.
One final issue: the game is too long by about 20%. Its rare that I complain about a game's length, but the main motivation for playing this game (finely tuned encounters/strategy; not the story) wears thin past the 60 hour mark.
So, to sum up, this is a game with old-school sensibilities (and problems) that is very finely tuned, challenging and beautiful to look at.