Brush up on the history of westerns in the movies. They will help you understand where its archetypes came from and how they changed over the years. Look at early silent films starring the likes of Tom Mix - they were often very simple right vs. wrong morality plays. Then examine how the works of John Ford and his generation added complexity and nuance to that formula. Watch the spaghetti westerns created by Sergio Leone and study how their dramatic extremes and amoral characters reinvigorated the genre. Finally, take a look at the decline of the western in the 1980s and how its subsequent resurrection after "Unforgiven" changed people's perceptions of what a western could be.
Understand how the western setting affects the storyline. Westerns are defined most strongly by their setting: a wild, lawless land slowly being tamed by hardy settlers. Traditionally, that setting is the North American frontier of the 19th century, but a number of other locales carry the same traits. "The Proposition," for example, is a western set in 19th century Australia, while "Star Wars" is often described as a western in space. Japanese director Akira Kurosawa transplanted western tropes into medieval Japan so successfully that many of his films - including "Seven Samurai" and "Yojimbo" - were remade as iconic westerns.
Develop a storyline based on your setting. Within that basic context it could be just about anything - from a shoot-em-up action spectacle to a quiet dramatic romance. Most Westerns concern themselves with the notion of law vs. lawlessness, and how people define and defend morality in a land where survival is never guaranteed. Your story should have a coherent beginning, middle, and end, with a rising dramatic arc and a suitable climax for the finale.
Flesh out the characters who participate in your storyline. Give them personality, motivation, and reasons to be in conflict (or allegiance) with each other. Most importantly, they should each have an arc, representing the changes they go through from the beginning of your screenplay to the end. You needn't include every detail about the characters in the screenplay; indeed, you should refrain from undue exposition, but it helps to know where they're coming from in order to make them more believable.
Write a draft of your screenplay, covering each pertinent scene in order. Keep an eye on the length. Screenplays roughly translate to one page per minute of screen time. If you go longer than two and a half or three hours, you're liable to bore the audience.
Revise your screenplay several times by looking for places where it can be tightened and sections which don't flow as well as they should. Check the storyline for logical gaps and brush up any dialogue that feels clunky or awkward.
Give your screenplay to a trusted friend or editor and ask him for constructive suggestions. Apply any of his comments that you believe are pertinent and revise the screenplay again in order to address them. You should be left with something resembling a final copy.