The Fusion mechanic returns in the game as Execution. New terms aside, the mechanic is generally the same as the systems used in Persona 3 and 4. There are 21 different Arcana types in the game and there’s a fixed formula in combining various personas to unlock even more powerful ones.
Persona 5’s fusion system is far more generous since this time, it allows you to specify which Skills will be carried over to the new persona even before confirming its creation. The Twin Wardens (Strength) confidant will require specific personas with specific skills in order to rank up so this feature is a god-send. Take note that not all skills are available for inheritance.
First, let’s tackle the different fusion types in the game. New fusion types will be unlocked as you progress in the story and increase Igor’s confidant rank (Fool). Some of the most powerful personas can only be acquired via Fusion so using this system extensively will affect your combat strength all throughout the game.
This is the first fusion you’ll unlock and will be the one you’ll use the most. You just need to combine two different personas to create a new, more powerful one.
This requires three or more specific persona to produce a fixed resulting persona. Since the required personas are already indicated, there’s no chance of producing something else.
This convenient option allows you to see which personas you can create from the current personas in your possession. You can sort this by arcana or better yet, by level. The material personas will be listed on the right side for reference, as well as your character's level. You can also conveniently identify the personas you haven't unlocked yet since they'll be tagged as "New" on the left side.
This allows you to select one Persona to “feed” on another persona to increase its power. Though this can only be done once per day, you can sacrifice as many personas you want per session. You’ll get bonus EXP if the personas you sacrificed are the following:
Select one persona that will be used as a material in transmuting another object into a new skill card, weapon, accessory, or protector.
This fusion requires online connectivity and can only be done once per day (in-game). This allows a selected persona to transform randomly into another persona.
For basic fusion, you can refer to the chart below for more information. There are still some pointers you have to consider:
(Chart reference: http://spwiki.net/persona5/wikis/393.html)