1. Dont argue...when you argue with a difficult student you bring their stature up to yours. They win. Worse, it makes other students think they can argue with you too. Winning isn't even the point with these students, improving their stature in the class is exactly the point.
Instead: When you must speak with a student, do it in private. Outside the door works great. When a student is removed from the class he loses his audience. You imediately are in a position of control. If he starts to argue, don't get pulled in. Instead state what was done and how it goes against classroom rules. Give a couple of ways the student can improve. I always ended these little "talks" with a handshake and the words, "I know you can do better, I have confidence in you."
2. Yelling and lecturing makes every kid in the class dislike you. When that yelling and lecturing is aimed at one student in particular, it is a guarantee that their behavior will get worse. Worse yet, when ridicule or blame is used by a teacher no student feels safe. They could be next!
Instead: Be proactive by emphasizing problem-solving instead of punishment. This will help you avoid that horrible win-lose conflict. When all students are treated respectfully, even when they misbehave, it tells all of the students in the classroom that you are in control. Teachers who emphasis and reward acceptable behavior more than poor behavior get better behavior in their classroom. You get what you reward. When you yell, argue, and loose your cool with any student that is their reward. You'll get more of that behavior too.
3. Don't try to get that difficult student to give an explanation for their behavior. Demanding an explanation makes that student REALLY dislike you. The result is more bad behavior. Plus you won't get a real explanation...ever.
Instead: Give the student a chance to respond. Don't demand it, but give them the opportunity. Explain exactly what is being done wrong, and a couple of strategies to improve. Consider if this student needs academic survival skills. He or she may need direct instruction in communicating, sharing, and listening. It seems basic, but I've had many kids who absolutely didn't know how to do these things.
4. Keep your cool! When difficult students know they can push your buttons, they will push! What's worse, other kids will do it too. That includes sighs and eye rolls. It says you don't have control and causes tension in the classroom.
Instead: take a deep breath and stay calm. Keep in mind that the child doesn't act up just for you, it's a patern of behavior. Make sure the student knows you like them, but not the behavior. Sentences like "That kind of behavior is not acceptable in this classroom.", etc put the emphasis on the behavior, not the child. Avoid sentences that start with "You".
5. Don't ignor unacceptable behavior. When a student knows he/she can get away with it sometimes, the poor behavior will increase. Remember Pavlov's dogs? It's the same thing with kids.
Instead: Make sure the rules of the class are clear and posted somewhere in the room. Have consequences also posted, so the results of poor behavior are not a surprise. Practice what the behavior looks like, and what the unacceptable behavior looks like. Kids love roll playing. Then discuss why the poor behavior is a problem and what will be done. I would often include the child with the most behavior problems in the roll play, both in acting correctly, and incorrectly. It's a safe way to learn important rules. Avoid calling behavior "good" or "bad", instead use words like acceptable, disruptive, and so on. Once the rules and consequences are clear, put them into effect consistently with every student. No favorite here!
The truth is there are some kids that just do not respond to anything you do. They are chronic behavior problems. Remember that we can help most kids, but not all. If you need help ask for it. The child may need to be tested for a behavior disorder. If so, get that in motion.
One technique that worked for me was having a child with a particularly big issue call their parents and discuss what is going on. Always tell the parents that this could happen at some point in the year. It should not be a surprise that this could happen. The point is to help the child address the issue, and keep parents in the loop. I have to say, kids who would NOT admit to any poor discipline choices broke down in tears and regret on the phone with Mom. You do need to know the parents support your efforts. Calling a parent who is also a problem is usefless. I then get on the phone to tell the parent how proud I am that the child has owned up to the problem. I want the child to know I like them (and the parent as well). We discuss what might be done, and is acceptable to the parent. Usually Mom takes the ball from there, and I can let it go. Do NOT do this very often. I saved it for big problems only. It must also be done privately.