How does cognitive behavioral therapy work?

I understand the basic concept of behavioral therapy, but how does the process unfold?
I have never done CBT, although it is one of the highest recommended treatments for OCD. I’m looking for a new therapist but (obviously), I’m afraid.
Does it start with talk therapy? How do the exercises increase in frequency and difficulty?

How is CBT different from forcing yourself to ignore your anxiety and push through things? In my life, I’ve always found that pushing myself through my anxiety just leaves me feeling exhausted and depressed. Is CBT more effective than just “facing your fears?”