Determine a target age range for your play. Keep this in mind during the brainstorming and writing process, primarily using words and concepts that such children will likely understand and explaining those that they might not. If you know any children that are in your age group, show them your ideas and script excerpts for feedback as you develop your play. Reword any passages that confuse or bore your test audience.
Choose a theme or topic for your play. This will unify the drama and give you direction as you develop the plot. Dealing with issues that are important to children, such as understanding people who are different, death, friendship, a sense of place and growing up will draw your audience in and help them relate to the characters onstage. Don't feel the need to provide a pat answer to such important questions, however --- no major theme can be summed up with a simple moral.
Choose your characters and begin developing the plot. Every drama needs a major conflict, whether internal, between people or between a character and the natural world, to keep it moving. This conflict slowly builds, coming to a head at the story's climax and is resolved --- or left unresolved --- in the conclusion.
Make a list of the scenes in your play. Each scene should involve characters with conflicting goals, resulting in some kind of negotiation, whether over status, a physical object or anything else. Negotiation is the easiest way to show conflict onstage and keep the plot moving.
Begin writing your play, one scene at a time. Don't talk down to your audience, but don't write over their heads, either. Children are not stupid, they simply have a smaller base of knowledge than most adults. Run your script through an online Flesch-Kinkaid readability test to ensure that your audience will understand it. Read your dialog aloud to test whether it sounds convincing, making changes until it works.
Keep the drama exciting. Avoid long monologues, instead using quick dialog and leaving room for plenty of action. At the same time, write your stage directions as simply as possible, skipping them altogether whenever possible. The more staging freedom you give the director, the more likely your play will eventually be produced.
Stage a read-through of your completed draft with the parts played by children that you know. If your script calls primarily for adult actors, ask a few extra children to listen as an audience. Talk to the kids afterward, finding out what worked and what didn't. Rewrite your play in light of this advice.