Read a lot of existing crime short stories. There is little that can teach you "how to write" better than reading a lot and getting a feel for the styles and nuances of writing that you enjoy.
Gather ideas and inspiration. This is where you will need a notepad and pen --- you never know when a good idea will occur. The last thing you want is to let the idea get away because you didn't make a note of it at the time. Remember the old cliché about writers going to sleep with a notepad and pen next to their bed.
You can also get ideas from people you know who might work in a related field, so speak to your friends in the police department or your cousin the private investigator. You never know how valuable a resource they could be.
Give your story a beginning, a middle and an end. All stories follow this very basic arc --- and with good reason. It is a tried and tested formula. Once you've broken down your story into these three "acts," then break down each act further into a series of more detailed events. Remember that there is nothing to say that you must tell the story in that order. Filmmaker Quentin Director is renowned for jumbling up the running order of those three acts to great success.
Get to know your characters. It is a good exercise to write out a brief biography on each character. Know as much as you can about what motivates your characters, what are their jobs, who are their friends, how do their lives connect. You don't need to include this information in the story, but it helps you to know more about the characters and can have a clearer idea about how they will react in a given situation.
Limit the scope of the story. Remember that this is a short story and, as such, you should try to limit the duration to a short period of time (perhaps days, perhaps only minutes) and try to stick to only one plot and no more than five characters.
Choose a perspective from which to tell the story. Most stories are told from either a first-person or third-person perspective. In either case, think about who is telling the story. Is it the old maverick detective telling us about his last case before retirement or a career criminal lamenting on the mistakes he made leading up to his arrest?
Write a time line of events. It doesn't have to be especially thorough, but putting events into a basic order can be an extremely useful process.
Start writing. No matter how much planning and preparation you have done, the only way to write a crime fiction short story is to actually sit down and write it.
Revise and redraft. Correct any grammatical and spelling errors or inconsistencies in the story.
Send your short story to some trusted friends or colleagues to test read and gratefully accept their feedback.
Write your final draft taking into account any feedback from your test readers.