For anxiety, CBT must include one important component – exposure. Exposure just means practice doing things that have been avoided, in small steps, in real-world situations, with the help and guidance of the therapist. If you are working with a CBT therapist for help with anxiety, this should be a major part of the treatment.
CBT typically involves 16-20 sessions and it is very goal-oriented - the goal being to reduce symptoms and improve functioning in the target areas. If there are multiple problems (like depression and anxiety) or the symptoms of anxiety are very severe and it has been going on for many years, it may take more sessions, but you should be able to start seeing positive changes within the first couple of months.
In CBT for anxiety in kids, parents are very much part of the team. Parents are shown how to encourage practice and not give-in to avoidance or reassurance at home. In this example, if parents were asking the teacher for accommodation to write the report instead of read it in front of class, or let the child miss school on presentation day, the therapist would help them encourage practice of small steps (like have them practice in front of them a few times, then ask the teacher if they can practice 1:1 first before doing it in front of the class) instead of avoidance. Although avoidance helps people feel better quickly it does not help them overcome their anxiety (and actually makes the anxiety stronger). Anxiety can be overcome, and CBT is a great tool to help people do just that.