Are you a student? There are competitions such as KCACTF (a nationwide college competition) where you can submit your screenplay or one-act to possibly win awards/scholarships.
For additional exposure, check to see if any community colleges with theatre departments would be interested in putting on your play. This is also a good idea if you are writing a movie; putting up notices at local colleges can be a way to gain exposure, as most AV and Theatre majors have to, at some point, produce a movie of some kind.
Also, check local theatre groups. Some of them can be open to showcasing new plays/talent.
As well, you might want to pick up a copy of the Hollywood Creative Directory. Screenplay writing friends of mine swear by it.
Remember, screenplay writing is an extremely competitive market; do not be surprised if you receive multiple rejections before you get a bite. Trying the baby steps first will also gain you some additional street credit, so that when you do submit you can say, "These are the movies I've made," or "These are the awards I have won."