Coming to class and reading the textbook are both essential for a complete understanding of the material. One is not a substitute for the other since they are intended to complement each other. In particular, you should not expect every detail from the textbook to be explicitly presented in class—that would ultimately be an inefficient use of our time together.
In class, I'll paint with broad strokes, developing a general landscape for the ideas. Then, the textbook will help you fill in the finer details. Finally, working on the problems will help you put on the finishing touches!
This may take some getting used to if you haven't experienced it before, so here is a list of recommendations.
Make attendance a priority. You should make an earnest effort to attend every class period. While in class, listen actively and participate to the best of your ability or comfort level. You can expect to encounter the main ideas from the relevant section(s) to help build your conceptual foundation and intuition, but some details will be left for you to read in the textbook and to practice outside of class.
Take notes in your own words. There is rarely a need to copy notes verbatim. In fact, passively writing notes in this manner is a relatively poor learning mechanism. Instead, try to focus on what is being communicated. Identify, translate, and synthesize the main ideas as best as you can and include any questions or confusions to ponder later. During reflection periods or after class, review your notes and try to briefly summarize the topics we discussed. See here for more about note taking.
Read the textbook. Yes, you really are expected to read the textbook. The textbook contains more examples and more detail than we could ever hope to cover in our limited class time. Some sections may not even be discussed in class at all! Before class, skim the relevant section and problems to see where we're headed. In class, pay attention to those topics that seemed particularly difficult as you skimmed. After class, take a closer look at the section and read it carefully (more on this below). Finally, dig into the problems and exercises, referring back to the textbook and other resources as needed.
Engage with the textbook while you read. Avoid passively rereading information—otherwise, you may find yourself able to recite aspects of the material but not actually understanding anything. Treat your textbook like a workbook. As you read, have some paper available for notes, scratch work, pictures, questions, comments, or anything else you feel the need to jot down. When you come to an example, try it on your own before looking at the solution. When you come to a definition, try to come up with your own examples and/or counterexamples. Take regular pauses to make sure you're really understanding the explanations, filling in any gaps or rewording them in your notes if needed.
Discuss the material with classmates. Form a small group of peers to discuss material from the class and the textbook. Practice explaining concepts or solutions to one another or embark upon a group effort to overcome the more formidable problems. Collaboration can be hugely beneficial, even if only for moral support.
Ask questions and attend student hours. Student hours are the best place for you to get one-on-one, direct, personalized assistance and feedback from your instructor. Take advantage of this time regularly. Feel free to attend in groups and let me know if you can't make my scheduled student hours so we can find another time to meet.