Create your detective. Detectives usually have a few compelling characteristics that give them insights into their work. They are often quirky. Nero Wolfe, for example, never left his house and owned ten thousand orchids. Sherlock Holmes played the violin, wrote monographs on arcane subjects and practiced firearms indoors.
Work out your crime. There must be a seemingly insurmountable problem, which is why the process of detection takes some time. For example, a murder might take place in a room that was locked on the inside. Or a priceless jewel might be stolen from a roomful of witnesses.
Work out the solution to the crime--the method in which it was committed. Sherlock Holmes said, "When you have eliminated the impossible, whatever remains, however improbable, must be the truth." Create your loophole, know that it's conceivable, but keep it to yourself until the end of your story. It helps to work backward: Create the solution to the crime but reveal it in stages through the story.
Create your antagonist. The antagonist must have a unique motive for committing the crime, if a crime it is. Even if it's not spelled out, the motive must be available to the reader. A detective story must be interesting above everything else, and a unique motive goes a long way in the final payoff.
Create a friend for the detective, or at least someone with whom the detective interacts. This character is necessary for two reasons. First, the friend can showcase your detective's eccentricities. Second, the detective can explain her or his methodologies to this person. Father Brown often explains his philosophical reasoning to Flambeau, and thereby to the reader. Often, this character becomes the narrator, as in the case of Dr. Watson with Sherlock Holmes, or Archie Goodwin with Nero Wolfe.
Create other characters. In a detective story, there are many suspects. Give them possible motives. The motive often helps the detective find the criminal, so this is as important a step as creating the crime scene. Your aim should be to keep the reader guessing as to the identity of the antagonist, yet present the story in such a way that events make perfect sense when viewed in retrospect.
Create clues and alibis. A detective must use clues to solve his case; so must a reader weigh the clues in her or his mind while reading the story. Some clues may be fruitful; others not. Suspects may be cleared by alibis, and these alibis may in turn help the detective, or not.
Write your story. Remember that like all stories, a detective story needs an exposition, rising action, climax and resolution. In addition to this, a detective story usually has a resolution or denouement where the detective explains how he reached his solution. This is an essential part of the story, because this allows the reader to compare notes with the detective and see whether she or he solved it.