Well, it's quite easy—if you don't already know.
Modern publishing seems to have defied all the norms set for literature. Social media has had a transformational effect on publishing. Writers now opt for self-publishing platforms like CreateSpace. Even WattPad has millions of people writing their untold stories. This saves time and a lot of money. Not all of it, but it's cheaper than how things are done traditionally.
Poetry has evolved a great deal. Most successful poets can be found on Instagram and another well-known poets' community called AllPoetry. You get to learn some graphic design skills, those of the most basic level when making images for Instagram. Or you could put your poems on display on another platform called Mirakee.
There also are magazines that accept poetry and literature of all kind to publish in their issues. These magazines practically run on the contributions they receive. However, not everybody gets published. If you want to be nominated for those awards solely for poets, you need to start a reputation from getting published in these magazines. When you've enough experience and have been published in several places, you can mount the next step in your career as a poet and have a go at those awards. I know of Poetry Magazine and Rattle. There are thousands! While the only award I know of is the Pulitzer.
Put your search engine skills to good use and browse some more of both.
If you're an opinionist, you must know about Medium. You'll find professionals here who don't fret about not getting published in newspapers. Instead, the best enjoy a loyal, everlasting readership. People don't buy newspapers anymore; they read their news online. It's fast to start writing and expressing your views online than to wait for newspapers and other agencies to respond to you.
You can start your blog, too. It can a little difficult, getting people to find your blog. If you have a good know-how of SEO and algorithms, then you can be very successful as a blogger.
When it comes to blogging, there are too many variations and so much of depth. You get to write about whatever you know best. It can either be a travel blog, one about fashion, whatever you please. You can read other blogs, too, and go through a great learning experience. I recommend using WordPress. There are other platforms like Blogger. WordPress is the king of all the blogging platforms, though.
Writing and journalism have become easy. Anybody who's got the knack can do it.
Why stick to the system of getting your manuscripts approved while you have the internet to help you and you can pursue your affinity for literature in new, and modern ways? Even though the old ways have evolved, too, and publishing houses still exist, giving us some really great authors. You might want to reconsider this if you have studies and a job. Or worse, a family.
The takeaway, modern publishing is for those who don't have the time needed to have things done the original way. It may be technology-and-internet-dependent, but has advantages of its own.