All battle is one-to-one fight.
You and enemy will have three moves that need to choose 6 times = 1 turn.
How it works : Guard > Attack > Break > Guard..
Guard can counter after Attack with taking tiny damage, Attack can move before Break can do any damage, Break is slow but able to slam down Guard move with minimal efforts.
If you or enemy successfully hurt opponent 3 consecutive times will given chance to do "One More" for additional damage.
You cannot see all the enemy moves from start. To see more, you have to fight same enemy many times in order to unlock it (except the Servant battle, which is depends on Matrix Level you managed to unlocked).
This will be important in 2nd+ play because this is the one few stuff you can carry over.
Master have Support Skill (called "Code Cast") and Servant have own skill to use in battle which does not fit into Attack/Break/Guard move. Both uses own MP reserve.
To use skills..
Master can insert Code Cast or use item move during the selection phase. Can insert your move at any step but remember you can only cast spell or use item ONCE per turn.
Servant can use own skill at any step you choose, which will overwrite normal Attack, Break, Guard moves. Mostly damage but some have de-buff effect as well.
Noble Phantasm can be used after certain points in story have passed. It can be used ONCE per battle so think carefully where to activate it. It might need to use certain skills in order to use in battle.
You can only use skill that comes with equipment (can equip up to two) and Servant can lean skill by put points into stats while doing "Soul Alteration" in church (which opens up after the certain points in first week). If you forgot to do Soul Alteration, your servant will be weak as is (except the Health) so better to check in church after you have leveled up in Arena.