Establish clear ground rules from the first day of school covering the way that students will interact with others. Let students know that sarcastic remarks, ridicule and interruptions are not allowed in your classroom--and set an example by following these rules yourself. Setting limits will diminish the amount of rude behavior you will encounter.
Interact with parents from the beginning of the school year. Talking to them will give you a sense of the behavior guidelines at work in each household, and you'll know what kind of support you can expect if students are rude in class.
Find ways to praise students early in the year for quality assignments or for being helpful to others, and let their parents know. With many students, this will give them a sense that you care about them, and they will work hard to respect your classroom rules and may even lead others to act properly in your class.
Talk calmly and rationally with students who are being rude in your class. This is much more difficult than it sounds, particularly if students are mounting personal attacks. If you lose your temper, though, you will have lost-- even if you "win" by sending the student to the office. Keep setting the example for behavior in your room by treating students with respect and reacting calmly to disruptions. If necessary, take disruptive students out in the hallway to discuss their behavior without drawing undue attention to it.
Refer extremely rude students to the office. Profanity or fighting in class, remarks that constitute harassment, or damage to others' belongings are grounds for removal from the classroom in most school districts. If those things happen, refer students to the office immediately.