In order to be able to publish poetry, you have to prove to the publisher that your work is worth printing.
Here are some ideas for getting to that point with your writing, and then getting it published:
Join a writers group to get further feedback on your poetry and in turn help others.
Read and subscribe to alot of different journals to get an idea of which ones might fit your poetry.
Start off by sending your work to smaller, less well-known journals. You have a higher chance of getting published in those, and this will give you confidence. You could try sending poems off to a few well known journals too.
Submit your work simultaneously to various different places, and don't bother waiting for a reply. Just send some more somewhere else. Consider keeping a record of where you send your work.
Don't take rejection personally.
Write a professional and friendly covering letter to preface your poetry when you send it for publishing, include a very brief summary of your background and the subjects of the poems. Make it stand out
Check the websites of journals and publishers for submission information, and send them e-mails requesting information about publishing your work.
Check out poetry anthologies that might be looking for poems, these will look good on your CV. exercise discretion when deciding what to submit to who.
enter poetry competitions,the entry fee might be worth the exposure it gets you if you win or rank highly.
Consider conducting a poetry reading, start small to build up your confidence. Rehearse alot, and then read the poems slowly so they have time to sink in.
Consider self-publishing, there are many avenues for such activity. Try createspace or smashwords, you could then create a blog of your own poetry to help get it out there