Playwrights need to learn a variety of specialized storytelling skills in order to write effectively for the stage. Playwriting, in fact, is the art of writing for actors.
I suggest the following steps for emerging playwrights:
Become a theater person. Work backstage. Act! In fact, take acting classes. The actor is the playwright's most essential tool because the bottom line is this: what the audience perceives has to do with the performance of the actor first and the script second. I saw an exercise that proved this beyond a doubt. Actors from the Oregon Shakespeare Festival toured high schools and performed the local telephone directory. They performed everything from Shakespeare to James Bond, from soap opera to western, with no more dialogue than the names and phone numbers they found in the book. If this doesn't make a playwright realize that his essential tool is the actor, nothing will.
Learn dramatic structure. Study screenwriting for this purpose -- it's the most efficient way to learn beginning-middle-end storytelling, which is the storytelling mode in western culture. Learn the wisdom of the basic formula CHARACTER + OBSTACLE = CONFLICT.
Develop an ear for dialogue. Dialogue drives your story, so you must excel in writing it. You learn dialogue both by acting (learning to speak it, so you can apply the actor's test to your own dialogue), by listening (bus trips are great for this: listen to the cadence of human speech, the rhythm of slang) and by learning that stage dialogue is much more efficient, in dramatic terms, than "real speech."
Learn to write with suspense. You want to create a sense of "what happens next?" in the mind of the audience. Often you do this as much by what you don't write as what you do -- that is, you tease the audience, you play it like a fisherman landing a trout, giving just enough information along the way to keep the story moving, the suspense building. Boredom is dramatic failure.
Workshop your script. Ideally, every playwright should be in residence at a theater company (I had this fortunate experience for two extended periods in my career) in order to have immediate access to actors. Turn actors into active collaborators, live testing grounds for your material as it develops. If you become a theater person, then you will have networked sufficiently to do this. You can't write plays in a vacuum. Playwriting is collaborative by nature -- and you get to be the boss (unlike the screenwriter, who is relegated to a hired hand).
Don't over-write stage directions. Usually you are not directing the play, so let the director do his job. Only write stage direction that is essential dramatic action. Let the director block the movement of the actors and let the actors themselves add the personal gestures that will reinforce the lines.