Start researching the market and submitting to poetry magazines. Go the library and read the poetry journals to see what they publish and which best fit your work. Peruse markets online, and beware of scams. Competitions are not highly recommended, but can be motivational if you are aware of the practices behind the awards. With competitions, you are much less likely to be selected than if you submit your poetry outright.
Note that publishers will conduct an Internet search to see if your submissions are original, so anything you have posted online under a pseudonym is suspect. Include your online pseudonyms in your cover letter.
Writing is only half the battle. Marketing must be considered. The efforts go hand in hand, and you should also start researching the business aspects of professional writing. It's easier to work with this knowledge from the beginning.
Oh, Andrea has an excellent point -- in poetry, as in almost everything, WHO you know is important. So attending workshops and making contacts can benefit your aspirations. Don't be shy and wait for others to discover your talent -- you have to promote yourself. Acknowledge that you will most likely encounter rejection slips, and don't allow them to dampen your enthusiasm.
PS: Most poetry journals don't pay. And you will not make money as a poet, which doesn't mean you won't find yourself in a writing situation where you can make money, or at least get enough work published or submitted to allow for tax deductions if you reach that point.
Lots of luck and best wishes! :)