Finding a literary magazine that is willing to publish your poetry may seem a lot more difficult than other genres, as the opportunities available are harder to find, but it is not impossible. I have put together some tips and guidelines that should make the whole process a lot less daunting for you. 

Getting poetry published in a literary journal or magazine can be tough. It can feel even more difficult than finding a home for your fiction writing, as there tend to be fewer opportunities available for poets. But with the correct preparation, you will be able to find a publication that will be happy to place your work and pay you for it. So, if you want to see your poetry published, please read on.

As with writing any other genre, the most important first step is to seek out as many literary magazines and publications as you can and read them religiously. This is one piece of advice that you simply cannot ignore. The amazing Stephen King once said: 'If you don't have time to read, you don't have the time (or the tools) to write'. 

Reading these publications will give you an idea of what style of poetry is relevant and being published at the moment, as well as the standard expected from the editors. Lastly, reading a wide range of poetry will give you the inspiration for your own work while, at the same time, improving your poetry skills.

In addition to improving your writing skills, reading will also help you enormously with the research aspect of submitting your work. 

There are a few steps in the research process. 

Determine which magazines would be the most suitable for your writing style. 
What are their submission criteria? 
Where can you find these opportunities? 

Here are a few sources I have discovered but I am sure there are many more. 

Poets & Writers keeps a large database of literary magazines open to submissions. You can filter the list to include only magazines that accept poetry.
New Pages publishes Calls for Submissions regularly.  
The Review Review has a list of all magazines that accept submissions, simply use the filter option to search those publications that accept poetry. 
Duotrope is a paid service offering a database of literary markets. There is a free trial option so you can try out the features to see if you like it before parting with any money.

The above publications are open to submissions at set periods throughout the year, these are called 'reading periods'. 

When you are reading poetry publications, hopefully, you come across a magazine that seems the perfect fit for your own style of poetry. If you write about a certain topic then it is always wise to submit to your chosen niche magazine first, as you will have a far better acceptance rate than a more general publication. If you find a submission opportunity you feel positive about but your catalog of work does not fit the set criteria, remember you have two options. Either write a completely new piece of poetry that fits the style the publication is looking for or rework a piece you have already written to suit the criteria. 

There are also submission opportunities for poetry anthologies too; these are mainly based around a certain theme, but it is a good idea to keep an eye out for these too.

The key is to keep focused and determined and you will succeed. Whatever publication you choose to exhibit your work, I wish you the best of luck in your poetry journey.