My very simple (perhaps overly simple) advice: know your medium. There are many mediums for telling a story. You just need to know the strengths and limitations each medium has. A story is still a story. If the story has merit, it will work in (almost) any medium. With rare exceptions, there are some stories that simply can't ever make the leap from one medium to another. But I will assume your story is NOT one of those rare and un-leapable stories, and that your story is perfectly ambidextrous and can make that leap just fine. Concentrate on the strengths of the stageplay medium, and be very cautious with its weaknesses.
The three most basic mediums are Novels, and then Stage Plays, and then Screen Plays. Here are the super-simplified rundowns of those three:
NOVELS: A form of storytelling accomplished mostly via the internal thoughts and observations and reflections of the characters. Even those novels told via the limited omniscient third person narrator will sometimes get right into the head of a given character. There can be a lot of silence and stillness in a novel with lots of paragraphs dedicated to the meandering backstory regarding such things as the 10,000 year history of the geologic formation of a mountain range, or the dark legacy of a silver medallion handed down for five generations. These very silent pauses in a novel which take the time to explain stuff in excruciating detail don't always translate well to the screen or the stage (but can in rare instances). Internal thoughts of characters likewise don't always translate well to screen or stage. And as a general rule, voice-over narration in a film or a play is usually (but not always) looked down upon by critics as lazy cinema/stagecraft by a clueless writer and director. But you can work with these more difficult elements and get the gist in via other story-telling techniques.
STAGE PLAYS: A form of storytelling accomplished mostly via grand speeches and intense verbal exchanges between characters. And a three-act structure is preferable. Dialogue, dialogue, dialogue, and toss in a few monologues from time to time. Stage plays are VERY dialogue-heavy creatures. Action can certainly be done on the live stage, but flying through the air like Peter Pan or even like Superman (or even like Spider-Man, which caused a terrible injury to one Broadway actor a year or so ago when "Spider-Man" debuted on stage in New York) can get problematic. Aside from having to suspend actors on cables to help them fly, sword fights can certainly be done, but huge Lord of the Rings battle scenes are not so easy. Extremes of weather can also be super difficult (tornadoes and hurricanes) if the weather itself has to perform a specific action (like hurtling the Kansas farmhouse of Dorothy Gale up into the sky and transporting her to the Land of Oz). Fire can also be very problematic on stage, including and especially forest fires and volcanoes. Live animals can be almost impossible and will always be super expensive because you will have ASPCA representatives there to make sure the animal is being treated right, so employing mechanical puppet animals or else humans costumed as the animals is always preferable. (The stage play "War Horse" which Steven Spielberg adapted into a film had mechanical puppet animals in the stage play version, as well as people dressed as animals.) And learn the three-act structure! Some plays are told in five acts, but those are rare and very complicated to pull off. And one-act plays are so concise that you haven't a lot of room for either a huge cast of characters, nor very much in-depth stuff. If you do not know how to recognize and analyze the proper three acts, you MUST learn about it.
SCREENPLAYS: A form of storytelling told mostly through actions and movement. And a three-act structure is preferable. Movies must move. Go from Point A to Point B. Travel down the road to get to the goal. Take the MacGuffin to its intended destination. Move, move, move. The really difficult part of adapting a story to the screen is that the two key hallmarks of novels (internal thoughts), and stage plays (grand speeches and dialogue-heavy scenes), are considered anathema to cinema. Voice-overs for internal thoughts are deemed super lazy in cinema. And grand speeches are disregarded as amateurish and too on-the-nose. Now you can sometimes get away with those storytelling conventions in a movie, but unless you somehow pull it off in a way that's unique, it's hard to avoid the criticism from the army of film snobs out there. They want to see characters in action, not engaged in lengthy discussions about the desire to somehow eventually get around to the action. They want to see the wordless look of pain and anguish on an actor's face, not hear the actor talk about how pained and anguished he is. And learn the three-act structure! Films MUST have structure and can't wander around free-form the way a novel can.