Rule #1: Don't!
It is like a Catch-22. The fact that you're reading about how to go get published proves that it is too early for you.
It is important to understand that there is little or no recompense involved here. Glory? The only people reading your words will be others curious about what kind of stuff they have to write in order to be published there themselves. Bear in mind, too, that there are thousands of poetry magazines and webzines sharing very few readers.
There is also the small matter of poetry's condition. How many living poets can you name? More to the point, how many do you think even 1% of the population can name?
"Okay, then I'll publish a book."
See Rule #1. If you self-publish you will, at least, retain distributional control. This is to say that you can bury the product later, when you have produced better offerings. After foisting a few dozen copies on friends and family, the lesson shouldn't cost you more than a few thousand dollars--less if you use LuLu.
Planning a book is not just wrong, it's exactly wrong. As they say, the journey of a thousand miles begins with one step. Instead of trying to fill a volume with, say, fifty mediocre poems, try to produce one stunning critically acclaimed masterpiece. Think quality, not quantity. Bear in mind that, aside from the players' parents, no one wants to watch Pop Warner football when they could be watching the NFL. You will be competing against the best poets in the world. It is important to view this as challenging more than daunting.
How to Produce a Stunning Critically Acclaimed Masterpiece
1. Learn the craft.
You don't make it into the National Hockey League by skating on your ankles. Craft might not help so much with editors, few of whom have studied it themselves, but it will capture the attention of geeks--any one of whom can create a buzz for you if suitably impressed--and listeners.
2. Respect the craft.
If you don't know whether "The Red Wheel Barrow" is free verse or metrical you can learn. Start now.
If you don't care whether "The Red Wheel Barrow" is free verse or metrical you can't learn. Stop now.
Not writing. Never, ever let anyone see you reading poetry--especially your own--aloud from a script. That would be tantamount to announcing that nothing you write should be taken seriously, even by you.
It follows that you must either perform it or attract the attention of those who can.
4. Say what you need to say.
And nothing more. Ideally, it should be something small that could unfold to something different, something bigger. Avoid clichés and well-worn themes. Use original language to conjure up something interesting.
The idea is to attract listeners, not to repel them. Choose words that people will not only want to hear, but to remember. Verbatim. Let the audience decide what to call and how to treat your offerings.
6. We need to develop performance, multimedia and social media skills or network with those who have them.
By far, the most likely way for an individual to reach a large audience is to have a YouTube video go viral. Here is where technique can mean everything.
7. Avoid any mention of hearts, souls, the abyss, or other overwrought abstractions.
8. Know that you have "arrived" when strangers quote you.
9. Avoid Seinfeldian ("So what?") poems.
If You Insist
If impatient or overconfident, here are some pointers:
Do a web search of outlets or go to "Poets & Writers - Literary Magazines". Look for what seems a suitable venue and then research it. Make sure the outlet is still in operation. Check out their reading period.
What kind of content do they like? As long as it isn't a diary entry, one can wow editors with succinct plotlines that end with an intriguing twist. If not too self-conscious, a clever turn of phrase can help. Humor always sells. Avoid propaganda unless willing to severely limit your options.
Whatever your expectations are, lower them.