This isn't a tip for during class, but for before class. Do the assigned reading before class so that you have a general grasp of the material and can determine if you have questions about major points. Reading before class helps you to anticipate the main points and the organization of the lecture. Familiarity with the material allows you to focus on your own questions and makes it easier for you to take notes on important points rather than capture the instructor's every word.
2. Use visuals, outlines, and handouts
Instructors often provide outlines, on overheads, black boards, handouts, etc. Use these as a guide to what's important to learn. However, realize that there is more to know than what appears on the visuals. Sometimes a professor will write a single word on the board and students will write that word in their notes. Guess what? The word alone will not help you; provide context. What does the word mean? What does it relate to? Why did the professor draw your attention to it? Remember that there is more to know than simply the visuals. Professors often (not always) draw students' attention to the most important information. But don't rely on them. Instead actively process the material and determine whether it belongs in your notes, regardless of whether it appears in a handout or overhead.
3. Pay attention to signal words and phrases.
Professors often give clues to what material is important by using signal words and phrases, such as: this is on the test (obvious!), important , remember, to summarize, to repeat, to conclude, and for example. Professors provide subtle and not-so-subtle clues to what's important. Pay attention.
4. Don't record every word.
Process the material. Some students write down every word the professor says. That won't help you when it comes time to study. Don't write it all without thinking or processing it. Try to determine the important concepts. For everything you write, note the details, why it is important, how it relates to other materials, and include an example. You may not have enough time to include all of this information during class, but immediately after class spend 10 minutes reviewing your notes to add details and link ideas to other information. You'll be glad that you did so - especially when it comes time to study for an exam.