There are two extant accounts of the trial and death of Socrates by his near contemporaries, the Memorabilia by Xenophon and three dialogues by Plato, Apology, Crito, and Phaedo. As the character and death of Socrates are portrayed somewhat differently in these sources, your first choice will be whether you wish to write about the Xenophonic or the Platonic Socrates.
Next, you need to think about what events you will cover in the story and what your focus will be. Is your interest the trial, the time in prison waiting to die, or the time between his drinking hemlock and his death?
You will need to choose a point of view as well. Will you be writing from Socrates' point of view? That of some other historical character (one of his family or friends?) Or will you invent an imaginary narrator? Techinically, you will needd to decide if your narration will be in first or third person, and if third person, whether limited or omniscient.
Finally, you need to think about the timeline of your story. Are you writing in present tense as the events unfold (and explaining the backstory with exposition or dialogue?) Is your narrator living after Socrates' death and looking back?