What are parents to do if their child tells them that he is being bullied?

First, listen; gauge the seriousness of the incident and whether there is a history of such bullying.
Then find out what has been tried and work out options with your child – such as being more assertive, avoiding people and places, and seeking help through the school.
It is tempting to confront the bully’s parents or even the bully. Don’t. It seldom pays and commonly makes matters works. When bullying occurs at school, work through your teacher and principal.
When help is needed, call on the school. It has the prime responsibility for keeping students safe. Schools can help, especially if parents work closely with them.1
One of the most important things that a parent can do in this situation is to talk with your child. Tell your child that you are concerned and that you’d like to help. Here are some questions that can get the discussion going:

I’m worried about you. Are there any kids at school who may be picking on you or bullying you?
Are there any kids at school who tease you in a mean way?
Are there any kids at school who leave you out or exclude you on purpose?
Sometimes, more subtle questions are needed:

Do you have any special friends at school this year? Who are they? Who do you hang out with?
Who do you sit with at lunch and on the bus?
Are there any kids at school who you really don’t like? Why don’t you like them? Do they ever pick on you or leave you out of things?
It is also important that parents talk with staff at school. Share your concerns about your child and ask the teacher such questions as:

How does my child get along with other students in his or her class?
With whom does he or she spend free time?
Have you noticed or have you ever suspected that my child is bullied by other students? Give examples of some ways that children can be bullied to be sure that the teacher is not focusing only on one kind of bullying (such as physical bullying).2

Ken Rigby, Children, Parents and Social Bullying
Stop Bullying Now! U.S. Department of Health and Human Services. Warning Signs that a Child is Being Bullied.