Regardless of how quickly you can take notes, it won't matter if you are not prepared to learn. Above all, do the required reading before class. If you are unfamiliar with the material in the lecture, your notes won't be helpful. In addition, review your notes from last week's lecture right before class. Always bring your textbook and course materials with you in case the professor refers to something in the book. This will allow you to follow along and make a quick note of where the material is located.
Too often, students take notes that are too messy to decipher after the fact. Begin each lecture on a new page. If you take notes on a computer, open a new file for each lecture and title the files sequentially. Write down the date and the lecture's topic. Leave plenty of space on the page, including room in the margins for comments you might make when reviewing. Write legibly and bring highlighters so that you can emphasize any material the professor pays special attention to. If you think a particular example might help in an essay or might show up on an exam, highlight it.
While it is important to be organized, it is equally important to be efficient. You need to develop your own system of abbreviations and symbols for jotting down important material quickly. Some common abbreviations are "w/" for with, "w/o" for without and "b/c" for because. Come up with other abbreviations that make sense to you, especially for words that come up a lot (use "gov't" for government in a political science class). Use question marks in the margin to indicate any point you don't understand and need to review, and asterisks to indicate importance.
Taking notes successfully is not just a matter of copying down lectures and putting your notes away. You also need to review and sometimes add to your notes after the fact. Set aside time later in the day of the lecture to reread your notes with a highlighter and pen. Write comments or questions that occur to you in the margins. For some students, it helps to write a brief summary of the notes after class. Insert these into your binder or notebook, as they will help you review for an exam later in the semester.