Read young adult mystery novels, and research the age demographic for which they are intended. Classic examples of the genre include the Hardy Boys and Nancy Drew series. More recent examples include books by Joan Lowery Nixon and Daniel Parker. Read novels that feature young protagonists, such as Stephen King's "Carrie" and "Christine." Your book needs to connect with young adult readers, and you need to write from a young adult sensibility if you want your mystery to work.
Develop your protagonist. He or she should ideally be a little older than your intended audience: someone in their late teens or early twenties. The protagonist needs to be sympathetic, resourceful, intelligent and curious--someone mentally equipped to solve a mystery. Beyond that, you can establish any characteristics you like, but try to focus on the character's personality, rather than his or her outward appearance.
Create a mystery for your protagonist to solve: a murder, a robbery or some other crime that baffles the authorities. The best approach to developing the mystery is first to determine who did it and how, then trace their path back through the planning of the crime and pinpoint clues that the protagonist should find. List the clues and develop the time and place where the protagonist can find them. Give the reader a chance to deduce the crime without giving everything away all at once.
Write a one-page description of each of the other characters in the story: friends, neighbors, police officers and, of course, the culprit who committed the crime (who may also be among the protagonist's friends and neighbors). Devote a few paragraphs to each character's background, personality and motivation; this will help you distinguish them during the writing process.
Formalize the plot for your young adult mystery novel. Start with the discovery of the crime itself (and the protagonist's involvement), trace his or her path through various clues, and finish with the uncovering of the killer. Be sure to include plenty of suspense and action, as the guilty party seeks to stop the young detective from unmasking him any way he can. Your mystery should end with a climactic revelation, followed by a brief epilogue in which the protagonist reflects on his or her adventures.
Write a draft of the novel. Be as diligent as you can, and set specific periods within the week to work on it. Most young adult novels run between 40,000 and 70,000 words. The style should be sophisticated, but use reasonably simple language so that the core audience can get into it. Keep going until you finish; don't stop for rewrites or edits.
Set the book aside for a few weeks to get a fresh perspective, then reread the text and perform any necessary corrections, rewrites or polishing. Ask a trusted friend to read the text and provide constructive feedback on things you can change.