Final Fantasy II has a Character Advancement System unlike that of any other Final Fantasy in the series. The system is actually similar to that of the SaGa series. In fact, the designer of the SaGa series, Akitoshi Kawazu, designed FF2.
Moving on, what makes the Advancement System in FF2, is the fact that there are no experience point rewards at the end of battle. Instead, characters are developed by their actions in battle. A character who evades many enemy attacks will get faster, a character who attacks a lot will become better at attacking.
Weapons and Magic must be 'leveled-up' though. Any character can use any weapon or spell, but in order for them to be ultimately useful, the character must build skill in the desired weapon or spell. Each weapon and spell has a Mastery Level, displayed with two numbers(ex. 2-53). Once the number on the right reaches 100, the Master Level increases. Weapons and spells max-out at 16. Weapon points are gained by attacking with weapon of that type, and spell points increase by using the spell itself.
Now that that's outta the way, let's learn how stats are actually increased in battle.