Ray Bradbury once said we should remember our childhood vulnerability as we approach our writing. Remember the monster under your bed? How about the closet? Or even that mean bully or adult? Don't forget the vacation, the campout, or even (gasp!) the basement!
Monster: To scare you, the monster must have some human traits but not necessarily be human. Don't forget Frankenstein had a soft side, a childlike quality. That was the redeeming social grace which endeared him to us, yet all the while his raging anger was to be feared. Still, your monster need not be human. Stephen King used a dog, Amityville was a house and Bradbury used a town with a circus.
Graphic Violence: When dealing with children, the amount of violence must never be graphic. You can cut off someone's head, but you don't need to go into the gory details of the act. Our imagination will supply the proper amount of gory graphics for a violent scene to scare us, sometimes too much.
Anticipation: Without that there is no story. We read and all the while have created our little anticipated ideas of where the line is going. A good writer will lead you down the rosy path to scare the tarnations out of you from time to time.
Pacing: Notice I said 'from time to time' in the previous paragraph. You can't have high terror the whole time. You must pace your story, make it a roller-coaster ride of highs and lows. But remember, all during this time, there must be a niggling in the back of the mind. The reader has to be at the edge of the chair hoping and waiting for the next big scare.
Atmosphere: Your story should have a dark side. Most horror stories don't take place on a beautiful, sunlight day with birds and bees and white fluffy clouds. You can start out that way, but you want your reader to become scared of the shadows. Shadows are the writer's friend and the reader=s concern. Think about this: Even on a bright day, if someone jumps out of the bushes and scares you... that person came from the shadows of the bushes; a location you couldn't see before hand. This is the writer's advantage.
Your characters in the story are the actual ingredient some writers skim over in favor of the monster. Don't.
Hero (or Heroine): This is the person the monster has singled out. The monster needs to make our hero feel vulnerable and alone. Usually the creature will zero in on the one weakness or fear our hero has and then use it to the creature=s advantage. The depth of your hero's character is the crux of your story.
Friends: Not all your hero's friends should buy into the monster theory. By doing this there is more room for story advancement as the creature attacks those who don't or won't believe. Even when the monster is in the room, there should be those who don't believe or want to believe.
Adults: This is children writing specific. Adults are usually the enemy of children and therefore can't be trusted. Of course, there's a rule broken every minute. You'll have one adult who will believe -- if not help evolve the monster -- and could be crucial at the proper moment. This is the writer's call. Sometimes adults aren't involved in the story at all or play superfluous parts.
Non-believers: You just have to have the nay-sayers; what more can be said?
Plot: Your hero, no matter how grave the situation, must have an out; a reasonable, logical out. If you fluff your hero's escape, you'll lose your reader. I was once told by a writing friend of fantasy that when you put a wizard into battle, you'd better have a way out other than zapping him away. A proper wizard would never go into battle with the idea of zapping away when things got tough. This is true for your hero and monster. If things get tough, have an out for them to continue the story line; otherwise, kill the character at that moment.
Sex: Excuse me, you're writing for children. The only sex is boys and girls. Jeesh!
So there you have it. Shadows, lots of shadows, a good friend or two, a friendly monster of some sort who just happens to know your one major fear or fault, and a lot of people who don=t believe in you, but you believe in yourself and your ability.
If you need a bit more help, R. L Stein has a book or two out the kids seem to enjoy. Read them for a bit more insight.