Writing a play is a little different from writing a short story. A short story is complete in and of itself, while a play script is just the blueprint for a production. We'll get more into what that means later. Now, it's time to start!
...but what to write play about?
On my first day of playwrighting class in ollege, the prof made us write a list of every human being we'd ever known or met, however briefly, in our lives. He made us write non stop for 15 minutes, so these lists were very long. Then he told us to look over that list and identify a person on the list who had a very strong need. " Someone on this list needs to get something that they cannot survive happily without." Picking the person and identifying their need became the basis for our first plays.
If you want to write a play that works as a blueprint for a compelling production, you have to write a protagonist with a strong need for something. You don't have to pull from your own life, (although it's often easier to start that way) but you do need to figure out what your main character is trying to get.
I worked for a bunch of years as a judge for a high school one-act play competition in South Carolina, and te thing that crippled most of the plays was that no one needed anything. People were content to talk about stuff, but no one was doing anything. Those of you who took part in the Improv Intensive Training will reemember how many of our scenes stalled because peopl were talking about stuff, but no one was doing anything.
The second step will be to work out who/what is getting in the protagonists' way. Some writers like to work these two aspects together, others will be happier just starting by generating a character with a compelling need for a specific thing. (Does not have to be an object; could be a person, metaphysical, etc.)
Start with a character and a need. The play will follow.