Same approach as with a publisher or agent search. Get online or use a theatre/writers guide and look up theatres that present new work, work that reflects your own style of writing and themes etc. Become familiar with the market, see lots of theatre productions, read reviews, keep up with who is doing what. Check out each (the ones that are suitable) individual theatre's guide to submitting new work (usually found on website), follow those guidelines, put script in envelope and send it to the appropriate person in the format requested, usually the literary manager. Not all theatres produce new writing so become familiar with who produces what. Most mid size theatres produce some work in house, some exclusively so, the type of theatres who will not be interested are those who always buy in touring work.
You could also try getting an agent but most new writing theatres have no problem accepting unsolicited scripts and have a team of readers to deal with the work that comes in, all an agent does is get you to the top of the reading pile or to a literary manager without a huge wait. Become familiar with what is on in your area, local theatres tend to favour local writers. Keep an eye out for competitions, my first full production and first play was as a result of entering a competition and it lead to two further commissions. Join a theatre writers group in your area as they are a good source of feedback and opportunities. Attend events at local theatres such as post show discussions, go on courses (often run by theatres) get to know who the good directors are in your area and what they are looking for, get connected and informed.