It's very satisfying and gets more fun and deep the more you progress. Also it's quite a bit different in all the three games. I'll refer to Xeno1's combat for the sake of simiplicity.

Tldr: this is a good general explaination, also shows some general combat https://www.youtube.com/watch?v=c_DsUSxDm3M

This is just some random gameplay:

The basic gameplay flow consists in: Engage the enemy > draw aggro to the party's tank > use debuff skills > use damage skills. Throw in the mix a chain attack when possible, and repeat until the enemy is dead.

The party consists in two characters played by the cpu and one character controlled by the player. Everyone autoattacks automatically, and everyone is free to move around the enemy while doing so. The fun part consists in using the right skills at the right moment (if the enemy has a debuff) and in the right position (some skills hit harder or trigger additional effects if you hit the enemy from the sides or from behind). You have to be mindful of your skills because they (obviously) go on cooldown once used and because if you do too much damage the enemy will target your character (which is something you don't want, unless you're playing as Reyn)