Reach out to many people. Poetry is written from an intensely personal perspective. While it is unavoidably personal, it must also reach out to many people who are coming at life from many different angles in order to be considered for publication. Judging ones own poem is rather like judging your child's first piano recital. Why can't others see the brilliance as clearly as you! However, publishers are not attached to the heartfelt reasons you wrote each poem with such a personal longing. They are looking for poetry that speaks on its own, once it has left your paternal hands. Judge your poetry as objectively as possible. This gives you the best approach for editing or even discarding a poem. After all, once you begin the process of searching for publication of your poems, only the strongest ones will survive and even then, many will not. It is a competitive, subjective process that is not for those who internalize rejection too harshly. Rejection is a very big, unavoidable part of the publishing process.
Be careful of vanity or "subsidy" presses. One of the first venues you'll come across when doing an independent search for publishers are vanity or, more recently called "subsidy," presses. A vanity press is when the author pays for the publishing of his book. While there is nothing wrong with a reputable vanity press whose contract guidelines are clearly spelled out, there are some outfits out there who will take advantage of an author's desire to have her work published. A published book needs an ISBN number, and if your book is associated with an ISBN issued by an unethical vanity/subsidy press, getting it to reviewers and other marketing venues will be next to impossible. These scams will, perhaps, send a few copies of your book to a few bookstores but they do none of the necessary follow up and no meaningful marketing. Beware of any vanity press that makes pie in the sky promises of doing all the marketing for you. There are no free rides, and the world of publishing is no different.
If you are interested in self-publishing, be certain you can speak with someone at the publishing company in person to discuss the particulars. Read any contract thoroughly and ask as many questions as needed. A reputable publisher will never be bothered or too busy to deal with your concerns and inquiries. They will make sure your questions are thoroughly answered and that the contract you signed has been gone over completely. For new poets, the small presses are an excellent starting point. They are far more likely to give your work a timely, considered review.
If you are interested in having your work put out for the first time, one very positive approach is to research poetry contests from reputable literary magazines and institutions. Some awards are given to first-time poets who have enough work to compromise a chapbook. Chapbooks are small softbound poetry collections. Winning such a prize or contest can get your work out among the more mainstream literary venues.
You can also begin by submitting your poems to reputable literary magazines for publication. Be sure you read a copy of their magazine before submitting so you will know if your work is in line with what they typically publish. Be thorough when reading their submission guidelines. Publisher guidelines are in place for a reason and they are, as a general rule, very exact about having them followed.
Be patient and stay positive. Never overlook the "red flags" of a scam but never overlook the opportunities of valid, reputable publishers. Take your time and prepare for the disappointment of rejection and the thrill of acceptance. Quality poetry will find its rightful home in the hands of a good publisher and you will be glad you did your homework in advance!