Watch the original movie several times to get a feel of the story and its characters. If the movie is part of a franchise (several sequels already done) be sure and watch every movie in the series. If the movie is based on a book or novel, be sure to read it also.
Read the original movie script. Look for drafts of the script as the shooting script contains camera angels and other directorial instructions. Pay attention to the style of writing and compare what was written to the actual movie. Look for the scenes that were deleted from the final version and attempt to understand why. Did they not move the story or were they cut in order to fix a specific time limitation.
Pay close attention to each of the characters in the movie. Know who lives and who dies and understand each character's personality traits. The hero in the first film cannot become the bad guy antagonist in later stories.
Find a logical progression of the story line. Plot out what happens next after the close of the original movie. This is the best way to write a sequel because by continuing the story line, the audience will naturally want to know what happens next.
Write your script using proper industry format. Download CeltX, a free screenwriting program, or do a search for scriptwriting templates for Word. Writing in the proper format shows you are serious about becoming a scriptwriter.
Make sure your screenplay fits the allotted time. Determine how long the original movie was and trim your script to fit the same approximate time limits. Sequels are generally given the same amount of screen time as the original movie.
Have friends and family read your script when it is complete. Ask them to be brutal with their feedback of what works and doesn’t work. Rewrite using their suggestions.