Familiarize yourself with music theory and common song forms, if you have not already done so. Even if you do not plan to write the music to accompany your poems, it helps to know how songs are typically laid out, so that you can structure your poems to be set to music. You will probably want to write poems with a regular meter, for example, rather than free verse with an irregular rhythm.
Listen to already published songs in the genre you are interested in and think about what makes them interesting or unique, such as what kind of story they tell or what kind of rhyme patterns they use. Being able to identify what makes other songs appealing will help you to incorporate these elements into your own work; however, always keep in mind that your work needs to be unique and different to stand out from the crowd. Mimicking the form of popular music is not the way to go and is not likely to interest a music publisher.
Write or edit your poem to fit the song form of your choice. Think about factors, such as the chorus, verse and rhyming scheme. Even if you want to be inventive and create your own song format, think of what the song would sound like to a listener as you write the poem. Do not hold back anything; make the poem the best you possibly can. You will probably not be able to publish a poem that is merely not bad. To get a publisher's attention as a new songwriter, you need to have a poem and song that strike the publisher as being something people would pay money to hear.
Develop an original tune to go along with your poem by experimenting with chord combinations on a piano or guitar. You can also start the other way around and develop the tune before the poem. Again, it helps to read up on music theory and song styles before you get started, if this is not something with which you are already familiar. If you are not interested in writing music yourself, team up with a musician who can help you set your poem to music. Because there are so many talented songwriters out there, a poem will be much more likely to be published as a song if it already is a song. Music publishers are not likely to look at text that is not already set to music.
Register the song with the Library of Congress or otherwise create a proof of copyright. One simple method you can try is to mail a copy of the musical score and poem to yourself in a sealed envelope and file the unopened envelope away with the stamped date.
Create a demo CD with a performance of your song. If you are a competent musician, you may be able to perform the song yourself, even if you are not trying to market yourself as a singer. If you are not, hire musicians to create a demo. Music publishers will want to hear what your song sounds like before they decide whether they are interested in it.
Contact music publishers and find out their submission guidelines for demo tapes. Submit your songs according to those guidelines and see what happens. If your material is not purchased by the first publisher you try, do not give up --- try another one.