Choose the factual events that you wish to depict in your story. Choose events that deeply interest you to spark your inspiration when it comes time to write the story. Also, consider any overarching themes you wish to incorporate into the faction story later on. Although these ideas may change throughout the writing process, it's a good idea to try and develop them at the start so that you don't end up losing focus in your writing.
Research the factual events thoroughly. Look for multiple sources that give you different perspectives so that your story doesn't end up seeming biased. For example, to write a faction story set in the Vietnam War, research political analyses of the war from both sides of the conflict, as well as first-hand accounts from soldiers. This gives you a multifaceted perspective to draw from in your own writing.
Draw or write out a basic outline for your story. This is where you begin to think through devices such as characterization and plot development. Even if your story closely parallels a factual event, much of the story will still be fictionalized through the creation of dialogue and description. In your outline, begin to develop these ideas and map them out chronologically.
Write your faction story, keeping in mind your research and outline. As you develop your story, it will most likely stray from your original outline, and may even extend beyond the parameters of your factual research. However, it's important to not lose site entirely of your research and outline, as this may cause your story to stray too far from the factual events on which it is based.