My favorite job class throughout Final Fantasy has always been the Blue Mage.

So in hopes of honoring this class I have here for you five new methods for them to learn magic!

Blue Gil

When a monster is defeated, the Blue Mage may spend half of the gil they earned in order learn all of the monster's skills. In story the example could be making an offering of money to a higher power, or simply paying a mentor to help teach them the ways of the beast.

Blue Item Drop

There is a 30% chance that a monster will drop an item related to one of it's skills. (A goblin might drop "gloves" for Goblin Punch, and a bomb might drop "gun powder" for Suicide.) In story it can mean anything, whether the Blue Mage channels the spell out of the item or they simply apply it to them selves.

Leap

When in battle if one decides to Leap an enemy there is a 60% chance that your character will Leap the foe, and both you and your foe leave the battle. When the battle is over you learn the all the Blue Magic your foe knew.
However, during a boss fight, if you use leap you must roll a d%. If the result is 50 or higher you succeed, but you and the boss must remain in battle. You will learn the skills when the battle is over. In story this could mean that you studied its ways until you became fully absorbed or that you literally leaped on them while sucking the the power out of the monster as it ran off in terror.

Lich

Once you defeat an enemy you learn all of its Blue Magic. As a result you are considered "Undead".¹ The only methods of MP and HP healing are from Blue Magic and resting. In story you might be a lich, or your character is cursed.

Sky Ore

This is like lore but with a higher chance of success, but also with a price. The character may buy an item dedicated to absorbing a monster's skills. The item is called "Sky Ore". During a battle the character may use a blue ore and has a 70% chance of learning a spell at random (or whatever the master chooses). He may also choose to single out a particular power that he has already seen, with a 90% chance to learn that specific power. A Sky Ore costs 500 gil.
Optionally there is also the Midnight Ore which has a 50% chance to learn all of the blue magic from a foe for 1000 gil.
Another optional ore is the Nebula Ore which has a 50% chance to learn every blue magic from each enemy in battle. This (like X-Potions and X-Ethers) can only be found and not bought.

Hey, wait a sec: if you're using Blue Items, could they be stolen, or would there be a similar Tech for this purpose?

Well, there's the obvious "steal gold to use for Blue Gil method"…

New Command Skill: Hijack

Choose an opponent, then make a Magic attack roll; if it hits, the target loses the use of either the most recent Tech ability they've used, or a randomly-determined ability, for the remainder of the battle. If you are a Blue Mage, you may instead steal the appropriate Blue Item for the Tech. This Tech may only used once per battle OR per enemy type at the GM's discretion.