The Rage Form in Kingdom Hearts 3 can be a blessing when you are stuck in a difficult situation. When the Rage Form is activated you get a completely new set of attacks, and even a special attacked called Risktaker. This will halve your current HP, but deal huge amount of damage. This is great for certain situations, but it's also a huge risk, since you easily get to very low health.
So, how to activate Rage Form in Kingdom Hearts 3? You cannot really control it, but it will occasionally prompt you to enter it. When you get the option to enter it during combat, select it and hit Triangle / Y to activate it.
It seems that there is a higher chance that you will be able to enter Rage Form when you are low on both HP and MP, but there is no guarantee that it will prompt even if both of these are low. So there is a bit of luck to it as well.