CFT uses a "three systems" model of emotion: the threat system (fear, anger, anxiety), the drive system (goals, striving, achievement) and the soothing system (safeness, connection, calm). When the threat system is overactive and the soothing system underused, life becomes full of pressure.
Your therapist helps you understand where your self-criticism came from and what job it has been doing, without blaming yourself for having it. Then come practices such as soothing rhythm breathing, imagining a compassionate companion, writing a compassionate letter to yourself and developing a "compassionate self".
CFT can be used on its own or alongside other approaches such as CBT.