Read school policy. There is no consistent state law against children skipping a grade, but individual school districts will have their own distinct set of rules on the issue. It's important to be clear with your local school's policy before proceeding with helping your child skip a grade level.
Consult with the child's teacher, who will be the best judge as to whether the student is ready to skip a grade. The teacher will be able to assess both the student's scholastic aptitude and maturity level to determine if she would fare well in a higher grade.
Prepare a portfolio of your child's work and grades. If he engages in educational activities outside of school, include these as well. They'll help showcase the educational level of your child, as well as the maturity level, which is a big part of skipping a grade.
Schedule a meeting with the principal of the school. Explain why you feel that your child should be allowed to skip a grade and calmly listen to the principal's response. It's important for both the principal and the student's parents to understand each other's opinion. Also, if the child is allowed to skip a grade, permission will start with the principal.
Fill out the necessary paperwork. While every school has its own unique procedures, there may be request forms to file. Find out what the school requires and submit required documents.