Examine your poem. Figure out what type of poem it is and put it in a category. Some companies prefer rhymed verse while others only accept unrhymed poems. Other companies look specifically for humor or inspirational poems as opposed to holiday poetry or works that expresses sympathy.
Research the market. Publishers vary in what type of poetry they accept. Blue Mountain Arts, for example, only accepts unrhymed poetry or prose that focuses on friendship, love and other inspirational sentiments. Find a publisher that is looking for the type of poetry you write.
Choose a small publisher. For those just breaking in to the greeting card market, a smaller company is more likely to choose a well-written poem from a new author than a large established firm with a stable of writers. Companies like Papyrus, Portal Publication and Majestic Greetings might work as a starting point for your submissions.
Follow the guidelines. If a publisher asks you to submit by email, don't send postal mail. Examine the guidelines and follow them explicitly. Place contact information on each page of your submission.
Resubmit your work to other companies. If you find that a publisher does not want or need your submission, try other publishers to get your work out there. Be persistent and consider writing in other genres in order to expand your chances of success.