One way to get published is to take the traditional route. You write something wonderful, finish it up, make sure it's as good as it can possibly be, and then you start querying literary agents. Don't even think about contacting a large publisher on your own. As the system stands now, and has stood since God was a boy, there is no way you'll ever get through to an editor at a large publishing house unless you go through a gatekeeper...which is the literary agent.
If you don't know how to query a literary agent, you can start by checking out this link. This is a literary agent who offers free advice about querying that's always as accurate as it can get about the query process. This link is a good example of the query process, as it stands now.
There's also another approach. You can look into digital publishing and see what's been happening there for a very long time. You can check out this link to see what I'm talking about.
This is a publisher's blog where there are calls for submission all the time. You don't need a literary agent to contact them. You can do this on your own. Some offer advances, and they work exactly like "traditional" publishers work. The link I provided is only one example. There are many digital publisher web sites and calls for submission popping up daily for new authors. Silver Publishing, so I hear, is doing this all the time and keeping authors working round the clock. And I'm also hearing it's happening in all genres.
The last two novels I read...not including the Merv Griffin bio which is non-fiction and pure dish I paid way too much for...have been digital first books, written by new authors, and either self-pubbed or pubbed by a digital press. Both were excellent.
I'm not commenting one way or the other on which publishing approach is the best. That's up to the individual author, not me. We all have choices, and as responsible adults were are supposed to base our decisions on the information given to us. I'm just passing out information and showing new authors there are, indeed, choices.