There is not always a good way for students or teachers to reign in disruptive students.
Ignoring the disruptions and the disruptive behavior might be the best way for a student to help. If you don't talk to the people who are interrupting (or don't listen to them), maybe they will stop talking and pay attention.
Every student has a right to learn and every teacher has a right to teach. Students who feel like that right is being compromised should talk to the teacher about his/her concerns; however, if the situation isn't resolved, a student could make a daily log of events to help the teacher out. Write down specific interactions that block the learning process from taking place. After a couple of weeks, present the log to your teacher so that the teacher can add to it and present it to the principal. If there is a document trail that can be verified and shown to the students and parents of the guilty parties, then there is some backing to your request. Without evidence, there isn't much anyone can do. If both you and the teacher keep logs about the daily events and what happens, then you both can identify patterns of behavior that might help everyone to understand why things get so disruptive.
I have a set of codes which we agree (students and the teacher) as a class at the beginning of each term. We discuss the structures we need in place for the class to work. We usually include listening when a main speaker is talking (could be teacher or student), avoiding put-downs and negative comments, quiet when we are writing, etc. These do vary a little from class to class, but generally we establish a positive working environment. Anyone who can't abide by the code is reminded, or asked to leave if they are a persistent disruption. With younger studentswe write our rules in tehir books as a reminder to them and their carers what was agreed.
Unfortunately, there are always going to be those classes in which some students are disruptive because they don't want to work. Students who maybe need more help or need to focus lose out in these situations. I think it is ultimately up to the teacher to make sure the environment is good for learning; however, there are still going to be those kids who are loud no matter what (and they aren't doing anything particularly wrong, so it's difficult to punish them). As a student, you should let the teacher know that you might need a little more one-on-one attention, even if that means staying after.
This is a great question, and I'm sure you are fully aware that the solution is going to be specific to the situation.
Ironically, my most disruptive classes are the over-full honors classes, and at that, most often only 9th and 10th graders. These are students who have never had to work hard to make A's. Why should they think my class would be any different? In such a class, you would have done best to just sit down and be quiet when the rest of the class was talking. Trust me, you teacher notices, and loves you for it. Sadly, these classes are most often "punished" with more homework, more quizzes, more formal assessment, because there is such a lack of subject-focused discussion.
In other situations, I think it very highly depends on your relationship with the disruptors. I also agree that it is the teacher's job to maintain control, but once in a while, a student has the ability to diffuse a disruptive situation better than a teacher. Role modeling good behavior goes a long way, and this doesn't mean being the kid who sits at the front and answers all the questions. It seems being "smart" isn't exactly popular in most public high schools, but it could be, if, like Pohnpei said, enough "cool" kids were doing it.
It is very hard to control a class if you are a student. (In reality, students should not be the one responsible for controlling the disruptive behaviors of other students.) If you feel as if your learning is being interrupted, you need to speak with the teacher. Allow the teacher to take control of the situation for you.
You need to identify the students causing the disruption one at a time. If talking to them does not solve the problem, you need to give them some coping strategies. Many times the student just seems to feel he has a lot to say, and does not know how to be respectful and polite.
There's not a lot that any one student can do. A student has to think of his or her social standing. Trying to make disruptive students shut up does not always make one popular. The best thing a student can do is to try to ask interesting questions. If a student shows interest in a topic, it may influence other students to care as well. However, this works best if the student asking the question is seen as at least somewhat "cool" by the rest of the class. Having the class "brain" ask the questions is less likely to be influential.
Many times the reason students are disruptive is that they are not engaged. Many time the reason that students are not engaged is that the teacher has not managed to relate the content/lesson to the students in a way that is relevant. Just as teachers can redirect a student away from negative behavior towards more appropriate behavior, a student in the class who is annoyed by the disruptions can help the teacher and the other students make the content relevant.
Actually, a student is in a unique position to do this because they can better empathize with the descriptive student. For example, if a teacher is leading a discussion about a book that was written before students were even born, some of the students may feel that there is no point in reading the book. A student who is focused and who does see relevance in the story and who would like the other student to stop being disruptive can help point out the relevance to their peers. They can do things like ask questions that help the teacher talk about why this is relevant today, such as "Is it true that this applies to -blank-in our world today just like it did in the novel?" They can also overtly point out why something is important.
Redirecting someone to positive behavior is a more effective way to deal with interpersonal situations in general rather than berating their inappropriate behavior or telling them they are wrong without offering a positive alternative.