I have worked in the theatre industry as a performer for almost 15 years; primarily in Houston. The first thing I would say is each market is different. What works in Houston does not necessarily work in New York or L.A.
Wherever you go, I would suggest finding a group. I belong to Houston Area Theatre Artists on Facebook and I frequently see new performers introducing themselves. The members are generally helpful, recommending upcoming auditions or theaters that are currently in the need for performers. And over time there are audition notices posted on this group. This will get you plugged in to the community and making connections. A big plus that does make it easier to find work.
Unfortunately, you might have to work for free for a while. But this is normal for most actors (not all). I say unfortunately because there are so many talented people that deserve to be paid their weight in gold. But it's just the reality. And you might have to do it for a while to build up your resume and meet new people.
Next, look in any local trade publications for general auditions (cattle calls). It's a great way to be seen by many theatres at one time. Usually there is a nominal registration fee and you have to provide several headshot/resumes. The Alliance Auditions happen once a year in Houston and in the above group I mentioned someone will announce when that is. I believe it's in the Spring? It's been a while so I don't recall.
Once you start to get a sense of the Who's Who of theatres, look up the their seasons and do some homework. Reach out to those theatres you would like to work. And instead of emailing a theatre with "Hi, my name is Shelby and I want to work at your theatre. Here is my headshot/resume," be specific. "Hi, my name is Shelby and I noticed your are doing 'Cabaret' next season. As you'll see on my resume, I was lucky enough to perform in several Kander and Ebb musicals over the last few years, and would like to be considered for this production. I didn't see an audition notice on your website, but would someone be able to let me know where or when I can find that information?" Or something like that. That tells whoever reads that email you did your homework and are serious.
Again, this is one market. In New York it's a completely different animal. Still try to find a group; not only can you find possible work, but it's a good support system. And as far as the larger theatres, you would need to be a member of Actor's Equity to increase the likelihood of auditing, or have an agent, or be lucky.
The most important thing I can tell you is be ready. When a big shot comes along, you will be much more confident if you have polished songs and monologues ready to go on the spot. Or if you are a dancer, take classes to keep you body ready when necessary. Just keep trying and keep working hard.