Since you can't control but one character at a time and you can't control the actions of monsters at all, it's important to know how you can manipulate control over the AI, which will be controlling all characters that aren't under your direct control.
Generally, the AI will test out a variety of different abilities the first time it encounters a new enemy or when the Bestiary information of a foe is incomplete, in order to determine the extent of the of the enemy's resistances. This is why most first encounters will involve the AI (and the Auto-Battle option, which is controlled by the AI as well) selecting a combination of Attack and Ruin as a Commando or a seemingly random string of spells as a Ravager or Saboteur.
Once the AI has determined the enemy's affinities, it will proceed to select the most effective abilities.
Commandos will always choose the ability that deals the most damage based on their own stats and the target's resistances.
Ravagers will set up up abilities that best serve to maximize the Chain Bonus. If Enemy Intel indicates that an opponent is completely immune or absorbs certain types of attacks, the AI will refrain from using those kinds of attacks.
Saboteurs will use Enemy Intel to weaken opponents. If you identify an enemy as being susceptible to certain ailments under the "Notes" section (shown in-game), the AI will attempt to inflict that ailment first. Once all ailments have been inflicted, the AI will default to the Wound spell if available, or in certain cases, use Endless Nightmare to sustain existing ailments.
For defensive roles, AI behavior is less dependent on Enemy Intel.
Sentinels will always default to Provoke, unless the enemy is immune. Then, they will use their -guard abilities and will continue to do so until Provoke wears off. The AI will lean more towards counterattack abilities such as Entrench and Vendetta when HP is high, and then more towards defensive abilities such as Steelguard and Mediguard when HP is low.
Synergists will make use of Enemy Intel to strengthen allies. If an enemy sheet lists a favored type of attack under "Notes," the AI will focus on applying the corresponding Buff.
For example, if an enemy "delivers devastating physical attacks," the AI will first cast Protect on its allies and then continue to add more Buffs, giving priority to defensive Buffs when there are numerous enemies and then more to offensive Buffs when there is only one enemy.
Synergists in the Normal formation will first apply any all-target enhancements before refreshing them with single-target variants. Synergist monsters will use the Endless Blessings ability to refresh automatically refresh enhancements before they expire.
Medics will always prioritize the restoration of HP to over 70% (the point where HP is green) before reviving KO'd enemies or removing ailments. They will always prioritize the party leader over all other members in the party. If everyone is alive and in good health, the Medic will continue to heal by using a single Cure spell as needed. The gradual accumulation of Wound damage in difficult battles can make AI controls less efficient during drawn-out battles. Its focus on restoring health to over 70% can lead it to cast spells that are relatively useless since the Wound ailment has cause the overall amount of HP to decrease. They will also ignore more pressing concerns, such as status ailments. In these instances, manual control of a Medic can make a big difference.
In Final Fantasy XIII-2, you have the ability to tune your Paradigms so that you can have better control over AI-controlled characters. When you tune Paradigms, you can only tune the Paradigm as a whole, not the individual components of the Paradigm.
The Cross formation tells all AI-controlled allies, and the Auto-Command option, to focus on the same target. This is helpful when you want to apply status enhancements on a single ally, build Chains, or inflict status ailments on a specific enemy. Paradigms in the Cross formation are represented by the suffix -X (such as Relentless Assault-X or Cerberus-X).
The Wide formation tells all AI-controlled allies, and the Auto-Battle option, to focus on different enemies or allies. For Commandos and Ravagers, this option is very effective in fights with a large number or enemies. It's also useful in short fights where you want to use a Synergist's -ga Buffs, which give enhancements to all allies but don't last long. An AI-controlled Medic in Wide formation will focus on healing the entire party at once, which can be preferable in some battles. Paradigms in the Wide formation are represented with the suffix -W (such as Aggression-W or Delta Attack-W).