There are currently three ways to get more Ability Points in Kingdom Hears 3, and they are as following:
1) Level up to get Ability Points.You will occasionally get extra Ability Points when you level up your characters, so you will get some extra AP naturally by just playing the game and leveling up. However, you won't get AP every single time you level up.
2) Use AP Boost.The AP Boosts are a consumable item that can increase the Ability Point of the character you use it on. This item can sometimes be found in treasure chests around the in the game, but they are quite rare.
When you get an AP Boost, you can only use it on a single character to permanently increase the Ability Points by 1. However, you can save them for later if you want to.
3) Use The Skill Ring.The Skill Ring is an accessory that can be worn by the characters, and will increase their AP while using the ring. This ring can be purchased at the Moogle Shop, so stop by this place if you want to increase your Ability Points.
The extra Ability Points from using Skills Rings is only temporary, and you will lose the extra AP once you change to use another ring instead.