Write down key facts. It can take some experimenting to figure out what information really is helpful, so keep trying and don't give up. Different teachers do things differently.
Don't overdo it. Don't go crazy taking notes, trying to write down every word that's said in class. Some people actually learn better by listening, writing down a few key points, and then going over the material after class when they have more time.
Organize. Keep notes for each subject in one place so you can find everything easily when it comes time for a test. That may mean keeping a notebook or section of a notebook for each subject as you take notes in class.
Compare. Keep your notes handy when you're doing your reading assignments. Compare what you wrote with what the readings say — you may even want to add to your notes as you read.
Copy. You may want to recopy your notes when you get home. If you've taken notes in a hurry, you're more likely to figure out an unreadable word or sentence on the day of the lesson than you are weeks later when you look back over your notes in preparation for a test.
Ask. Don't be afraid to ask the teacher to repeat something you miss. If the teacher's going too fast, chances are your classmates will also be relieved to hear the information again