Familiarize yourself with the patterns and tropes of the genre. Read classics and modern books alike. Check out books such as Bram Stoker's "Dracula," Mick Farren's "Victor Renquist" series and Laurell K. Hamilton's "Anita Blake, Vampire Hunter" series.
Delineate your vampire mythos. Decide whether the vampires in your story will be repelled by garlic or not, whether they sleep in coffins or not, whether they burn up in the sun or not, and so on. Create a chart with their habits and physical requirements that you can refer to during the writing of your story.
Invent a main character that readers can relate to, whether he is a vampire, a victim or a vampire hunter. Give him believable strengths and flaws. Avoid making him a "Mary Sue," or an obnoxiously flawless cardboard cutout.
Come up with a premise for your story or a situation for the main character. Begin writing, and allow the plot to grow organically from the premise. If you are stuck, start with a classic vampire cliche (such as "a traveler happens upon a wealthy shut-in vampire in a castle" or "a vampire and a human fall in love") and let your own characters take over from there. Stop writing when you get to a place that feels logical to end the story. Only you will know when that is.
Read over your story for plot holes and inconsistencies. Make sure your vampire mythos adheres to the chart you made in Step 2. Fix any mistakes you find. Ask yourself, do my vampires pooh-pooh the fear of garlic in Chapter 1 and then burn holes in their fingers on garlic bread in Chapter 8? Tighten up the prose. Eliminate any plot elements or descriptors that do not feel necessary.
Show your story to a trusted friend or adviser. Ask them questions such as whether the characters feel true and whether the plot makes sense. If your vampire story is meant to be particularly funny, scary or sexy, ask them to rate their visceral reaction to it on a scale of 1 to 10. Consider their advice carefully and decide for yourself whether to take or leave it.