Just a short list of some words you might not be familiar with in the story... and some game mechanics being translated into somewhat real life written form.
Magic - Within the game, your characters have a Magic Points total which is used to determine whether or not you have enough energy to cast a spell. Similarly within the story, characters should try to keep in mind how much Magic Points they have. Every spell that one casts subtracts a certain number of Magic Points. Think of it as mental fatigue, smaller spells are less of a strain on their users, and thus can be cast many times with little effort, conversely, larger spells take longer and much fewer of the spells can be cast before a character would simply pass out from mental exhaustion. Even fighting classes will suffer the same effects from continual fighting, using their own set of abilities, though generally at a much slower rate then magic users.
Materia- is a form of pure crystalized magic. With very little training, most people are able to utilize the spells contained therein. The trade-offs are that in general, usage of the spells incur a much heavier MP toll on the caster and also the effects are generally weaker than what would be expected of a specialized caster with training and innate abilities.
Magicite- The solidified crystaline corpse of an Esper, Magicite retains a psychic impression of its previous personality. Telepathic communication can be established with the essence within, and it can teach its possessor magic that becomes innate to the character. In this way, a Warrior could learn Fire from a piece of Ifrit Magicite, and it would perminantly be one of his abilities. This takes a very long time. The second use is that, it can be used to summon its essence for a final attack that then shatters the Magicite and makes it worthless (even as Magitek fuel).
Summoning- The act of summoning requires that a budding summoner travel the world to various shrines devoted to those few Espers whom have remained in the world and establish a contract with them. At which point, the summoner becomes capable of calling the Esper into battle in order to aid the summoner. When a summoner summons somthing, it can remain for up to 30 minutes. It cannot be resummoned for 5x the ammount of time it was active for, and if it dies, it cannot be summoned at all until the next day. Summoning does not take MP, but it does tire the summoner, and it does require they do nothing but focus on maintaining the summon while it is active, this means attacking a summoner who is focused on maintaining a summon is an effective way to attempt to eliminate the summon. Thats what guardians are for. Summoners may also only use their healing magic on themselves, and their guardians.
Relics- there are more like traditional Fantasy RPG items. Magical boots that let you run faster, magical gloves that let you dual wield your primary or secondary weapon, enhanced armor that provides fire protection without needing materia slots. Relics are hard to find, but worth incredible value to many since they require no work or MP to function and work the same for anyone who puts them on.
Limit Breaks- Your limit breaks are expressions of your own character, learned through intuition, not teaching. They manifest in times of desperation and when your characters emotional stress level becomes too much to bear. They can be devistating attacks on single enemies... moderate attacks on an area of enemies, or somthing appropriate to your character. Magic using class' usually manifest one of their spells with a drastic increase in area or devistation, and Healers generally manifest healing or protective limit breaks that rejuvinates or protects the whole party. If your limit break matches this description, you do not need to confirm it with me. Limit breaks are as varied and unique as their users. In a writing sense, there's no need to really title your move just realize that most of the inhabitants of the world have these special abilities that tend to manifest itself in times of great need. Often times, these skills are pretty one-shot and aren't repeatable very quickly or often.
COMBAT- alright. In final fantasy, you have a number of HP. And until that number reaches 0... your basically capable of doing whatever you could do at full strength. This is because limiting your character as it is more damaged only serves to make it more likely you will fail the longer a fight goes on. In this story, most attacks that succeed in damaging you will still seem like glancing hits, unless they do massive damage, or unless youve already taken massive damage. Basically, keep combat realistic. It doesnt have to be a gore fest every time you engage a challenging beast. But nobody walks out of a fight unscratched in this story unless their taking on somthing much too weak to threaten them. Use that description to guide you when you describe your fights.