Good question. Let's suppose I get this thought: "Everyone hates me". In CBT we learn that the thought is irrational, for many reasons. CBT would then have you "correct" the thought by saying to yourself "that thought is irrational, everyone doesn't hate me, some people like me". In ACT we learn to stop believing this thought, thru cognitive defusion and other techniques. But even if we don't truly stop believing this thought, ACT tells us not to focus on the thought (or belief) but instead focus on what the thought is keeping us from. In other words, we stop struggling with the thought and instead focus on the avoidance the thought creates. To counter avoidance, we use mindfulness, values, and finally just brute willpower to move our arms, legs and mouth in the direction we want. It takes some reading and lots of practice, but eventually you'll stop avoiding and start living. While you're living, you'll feel anger, depression, anxiety, happiness, confusion, etc. That's called being human. Tolle and ACT teach that we need to learn how to just be a being.
CBT had me debating myself all day. With ACT, I treat thoughts and feelings like an abused puppy. I don't debate them or struggle with them. By dropping my side of the rope in an anxiety tug-of-war, I win by default.
ACT and Tolle also teach that we need to learn to be non-judgmental to ourselves and others.
Using ACT I've learned to become response-able. Sure I still screw up, but like the Japanese proverb says: fall down 7 times, get up 8 times.
I've printed business cards with the ACT algorithm on one side (in colors) and the FEAR algorithm on the other side (in just black ink).
Fusion with your thoughts
Evaluation of experiences
Avoidance of your experiences
Reason giving for your behavior