Acceptance and commitment training is a behavior therapy approach, and I don't at all claim to be expert or intent to do therapy online! But I feel there is element of simplicity of it I can try to explain, at least how I view it
In it's core it means uncomfortable feelings are part of life and habitually doing things to mute them can take you away from your true values. It means that you can let the feelings be and still do the committed actions towards their goals
Example
Personal Value:
1) I want better job, so I can purchase better health care for my family or go to nicer vacation
2) I want to be healthy eater and exercise so I can be good example for my family
Actions that take me close to my goals
1) Do presentations I need to do in work, upskill by taking more training and exams, cope with stress with bath and walks & breathing
2) eat healthy, exercise, sleep and so on
Uncomfortable feelings
1) anxiety, stress, fear of failure
2) I feel fat, uncertain I can really do it, I feel ugly and not good enough
Actions taken to avoid the uncomfortable feeling
1) don't sign up for training, don't do presentations
2) avoid or cancel plans, eat, drink too much
Most people get caught up in a cycle of uncomfortable thoughts and emotions and actions to try to avoid those. The assumption is When I feel better, I’ll do what matters to me. Uncomfortable feelings are part of life. It doesn't matter how slim you get, you will still get "I am fat" thoughts. Habitually doing actions to take you away from the uncomfortable feelings can take you away from the life you dream to live. It doesn’t work well for living a life that is meaningful, or moving towards your goals or values. Eventually we’re going to work on having those same thoughts and feelings and still taking the actions that are in line with your values and what matters to you
Am I taking actions away from uncomfortable thoughts and emotions?
Or
Am I taking actions towards values and what matters to me?
ACT does not suggest focusing on doing anything with your negative feelings. It is about letting them be and still doing the committed actions, steps toward the goals you have. It's about creating flexibility – when I have the uncomfortable feelings, can I still take the actions towards my goals. Creating some distance from your thoughts and feelings.
If the negative pattern is Uncomfortable feelings, actions away from thoughts and emotions, more uncomfortable feelings (anxiety, eat, anxiety eat)
ACT aims at uncomfortable feelings, actions towards your values, getting the values and what matter to you (anxiety, walk or prepare healthy meal, getting to live the life you want to live.
It's about letting yourself experience discomfort. Uncomfortable feelings are normal. You will be all right! You can still do what you have set your mind on.
There are a lot of books and podcasts on it, I can make suggestions but for example if you get a thought I am fat, I will never be able to do it. It doesn't suggest debating and questing the thought. One of the suggestions is creating distance for it. Repeating it adding I think I am xyx. I noticed I think I am xyz. accepting that negative thoughts are part of life. Saying all right, I hear you but let me get to the gym as I am busy now. Or repeating the thought with Donald Duck voice and having a little laugh at it