how can critical thinking skills help me to succeed in my speech class.

If you have critical thinking skills you are able to process knowledge in a deep and meaningful way. If knowledge is processed in this way, you can build upon prior knowledge, and draw conclusions from the information that is presented. Rather than just being able to recite the information, you can analyze, process, compare, synthesize and perform other higher functioning actions with what is presented.
So, if you are giving a presentation to an audience, and you see that they are not understanding the presentation, you can present the information to them in a different way that may make them more receptive to what you are saying.