A few of the Basics on Playwriting: character and character development, plot and subplot, plot structure, dialogue vs monologue, the much needed premise, et cetera.
Formatting your play: Proper formatting is an important skill. If your play is not formatted properly, literary managers, agents, directors, actors, and others may not read it.
Your skill as a writer: The use of symbols, analogy, metaphor, image, stage props, et cetera, can be the vehicles to create your dynamic play. Writing active, motivated, comedic or dramatic dialogue and monologues are skills and techniques you can use, coupled with stage props, to create various thematic and motivational levels for directors and actors to carry your story forward.
Self-Criticism: In order for your characters to succeed and your plat to be successful, you must be able to withstand and comprehend self-criticism. Identifying what in your script is good, what fits, and what works well, and what needs to be changed, set aside (never delete: save in a separate file), or adjusted.
Writing is rewriting: Along with self-criticism, editing and rewriting go hand-in-hand. “I am not re-writing! I’m not changing a line!” How many times have I heard that line?
The process using queries as a tool: Whether you want to or not, begin your re-write by reading your first page. Change the first words out of your character’s mouth from a statement to a question. What does it do to the progression of the story? (+/-) Does it move the story forward? (- / +) Does it create a problem where there is none? (+/-) Try it. If it doesn’t work... the least it will accomplish is that it will get you back into your play, by viewing it and your character from a different perspective.
Find a theater: Hosting a reading. A stage reading versus a staged reading. A stage reading: actors sitting to read before an audience without props or movement. A staged reading: actors holding scripts using some props coupled with stage movement or blocking. The latter is a little difficult, but well worth the effort especially if you have seasoned actors. In either incidence, once you hear the actors read and interpret your words, you and your reading audience will visualize the world you have attempted to create. Without a critique by the actors and the audience, you cannot advance the play to a full production.
What is your play about?: This should be a given. You must have a proposition, an hypothesis, a premise upon which your characters can to rely, after all they are the storytellers... if you don’t have a premise, they can’t relate to your audience. Many playwrights get mired in the muck of not knowing what their play is about. They don’t know what the focus of their play is: give your characters focus.
Write everyday: There is nothing like a writing workout everyday. Put a minimum of two hours each day aside to write. Find a time that is good for your imagination, get up ½ hour early and do it then or go to bed later.
Keep a journal: It doesn’t matter if you use an actual tactile journal, the writing pad on your phone, an app on your tablet, or your computer. The manner in which you record your ideas does not matter. What does matter is that you’re writing down ideas. By recording them they will stay with you and develop both consciously and subconsciously. I keep a journal of my wildest most explicit dreams: a great idea resource.
Writing is writing: Don’t just write plays. Try writing a Blog, or poetry, write short stories or develop a screenplays. All of this will help you be a better playwright.
Go see a play or several.
Read Arthur Miller’s plays.