It is difficult to get your work submitted, local theatre groups are more interested in performing known playwrights. You could attach yourself to the group with several other writers, or attach yourself to a theatre.
Another way is to try and create your own group. The trouble is that writers are not the best directors so it be better to keep things simple. You could attach yourself to a university -which the most famous writing and performing group Footlights (based in Cambridge, England ) was- a pub, a comedy club. etc. Or you just hire a church hall for a couple of weeks. It depends of course on what you can afford.
Competitions where you have to pay money to enter are not very likely to succeed, and so lose you money.
To start with it is very unlikely that you will be paid for your work. Maybe you should not just concentrate on play writing, but also novel writing, article writing, writing for TV and radio and so on. It helps if you also practice your writing to keep your mind fresh.
Of course in order to write a good play you need to be fairly knowledgeable about theatre convention-don’t come with anything too complicated to stage – Wagner may have wrote an earthquake in one of his operas, but that is rarely staged, and never by the amateur stage. Coming up with long bits of text may also prove unpopular-actors usually want shorter sections.
It also important you don’t include too many directions for how the actor delivers the words, it doesn’t the actor anywhere to go.
Good luck with your writing.
Paul Wimsett has self published work on Createspace and Lulu.com and also has had his work performed in a small venue.