Immerse yourself in the Star Trek universe. In order to write about it convincingly, you need to understand the ins and outs of its mythology--its history, its politics, the various alien species involved, etc. Until you know them and love them, your screenplay won't have the right air of authenticity to it.
Choose a point in the history of the Star Trek universe to set your screenplay. The original series with Captain Kirk and Mr. Spock took place in the mid 23rd century (2266 to 2269). Subsequent series such as "The Next Generation" took place over 100 years later, during the late 24th century, while the "Enterprise" show took place 100 years earlier in the mid-22nd century. Numerous changes and upheavals occurred over the course of those fictitious 200 years (the Klingons went from being humanities' enemies to their allies, for example), which will have a huge bearing on your action. It's worth noting that the eleventh Star Trek film is set during the very early days of James T. Kirk's adventures: about 2260 or so. If you want to keep in line with that, it may be prudent to set your screenplay during that period.
Develop a plot for your screenplay. It should entail some kind of galactic threat within the Star Trek universe: a supernova threatening to destroy an inhabited planet, an invasion of the Federation from an alien species, or the like. The threat should be specific to the Star Trek universe and present a considerable challenge to the heroes. If possible, stay away from science fiction clichés and try to find a truly original threat.
Decide which Star Trek crew is going to solve the crisis you have created, and the means by which they will do so. The specifics depend on the point in the timeline you selected in Step 2. If it's in the era of the Original Series, then the crew will be led by James Kirk. Later eras will likely center around Jean-Luc Picard's "Next Generation" crew, or possibly the crews from the "Voyager" or "Deep Space Nine" series. Since you're writing your own screenplay, you can also develop a Starfleet crew of your very own, consisting of entirely original characters (with a few exceptions; see Warnings, below).
Write up a draft of your screenplay, building the action around your chosen threat and your crew's efforts to find a solution. Keep the personality of the characters in mind as you write them, and be sure to include plenty of stirring space-opera-based action.
Revise your draft two or three times, streamlining the action and cutting out any scenes which seem superfluous. You want to shoot for a running time of about two hours, or 120 pages worth of screenplay.
Give your screenplay to a couple of trusted readers to critique: people who can be honest with you but provide constructive advice rather than just complaints. Ideally, you should let at least one Star Trek fan read it and one non-Stark Trek fan read it as well. If they both like what you're doing, then you're on the right track.
Finalize a draft of your Star Trek XII screenplay, addressing your readers' comments and adding any finishing touches of your own.