This question was asked on the Dr Jenn show on Cosmo radio on Sirius XM. Most of this response is paraphrased and expanded from the answer of Dr Jenn on that show, while the rest is personal experience and opinion. There are multiple levels to this answer depending on the type of teasing and even the gender of the child. Boys and girls tend to tease each other different as children.
Boys tend to do it as a show of aggressive dominance. One way to cope with this teasing is to show the boy how to stick up for themselves to the teasing person. Sometimes this display of power is enough to stop the teasing. However, you do not want to condone or support fighting.
For girls, it's far more subtle and manipulative, with the teasing girls tending to complete exclude the teased girl. This can be very difficult for the teased person to cope with because there is no good way to break up he group-think of a group of girls who are being coerced into excluding a girl.
So, the first level would be something like discussing the issue with your child about the types of teasing, why the teasing is occurring, and what they may be able to do to prevent it or turn it around. It's important to identify the source of the taunting: is it due to weight issues? Appearance? Socio-Economic Status? Hobbies? Sometimes, it can be due to something your child is doing that you didn't know about such as acting up in class, teasing other kids, or not playing nicely with others. This can be tricky and multifaceted, so it's important to try to probe past rationalizations and excuses that may be at the forefront to find any simple, teachable lessons that may be at the root of the bullying.
The second level may be something like talking to the parents of children who are teasing your kids or talking to all parents at some form of PTA meeting or similar grouping.
The third level is discussing the issue with the teacher of the class to see if there's anything the teacher can do to watch for and diffuse the teasing behavior.
The fourth level is discussing the issue with the principal. Usually for extreme cases of bullying, the schools have some resources available to help children. This includes stuff like adult shadows that will roughly follow the child around to diffuse bullying. The reason being that kids will generally not tease kids when there is a grownup around.
The fifth level if nothing has worked so far is to look into other schools in the area that may have better resources to combat bullying. This should be for only the most systemic, repeated, and severe cases of bullying. Of course, if you've made it this far in the process, then the bullying must be terrible at this point, and the previous school was dangerously negligent. At this tier there is also the opportunity for legal action against the school for not providing a safe learning environment for your child.
Overall, the most important thing at any level of this process is to make sure your child knows that you trust them, believe them, love them, and will protect them no matter what happens. When children know that their parents are behind them, their ability to withstand teasing is significantly greater. You want to resist overreacting, but you also want to resist just telling your child to "toughen up" or "deal with it" or "just ignore it" or things like that may show you as callous or downplay the issues the child is facing.