Get an idea. It does not have to fleshed out in order for you to jot it down. If a description of a person pops into your mind or if you cannot stop thinking about a scene from a dream, write it down. These ideas may serve as inspiration for a script.
Fall in love with playwriting. Go to the library and borrow many plays. Read them all from classic to contemporary and become familiar with the structure. Take a free playwriting course and learn about what makes a play work and come alive on stage. Practice your writing skills.
Write the play from top to bottom. As Oscar winners Matt Damon and Ben Affleck collaborated on Good Will Hunting, you can also work with a partner, or you can develop your own solo project.
Contact local playhouses and theaters. Speak to owners, directors, stagehands and volunteers and see about being able to put on your play. Being able to have your work turned into a performance will build up your confidence and give you more credibility and experience when contacting an agent to represent you.
Submit your work to competitions. Every state and most cities have yearly competitions for writers. Read the playwriting sections and the submission requirements. Many competitions will only accept unpublished work, so be sure to read all guidelines and regulations.
Check out the Writer's Market and the updated yearly version of the agents listing. Query an agent with the hopes of representation. Be sure to know what the agent is looking for specifically and how to pitch your play. Being able to market your work is extremely important. Be clear about the theme, plot and characters, while, enticing the agent into wanting to know more about the project.