Publication can take many forms. The refrigerator door is a good place to start. Or you could print out a copy and tape it to the wall above your desk, where you and your visitors can read it. Better yet, start a Blog on this site and publish here.
You could even start your own small press to help others get into print. Many well-known poets have started out that way.
If you're writing poetry as part of a class or other writing group, you may want to publish a selection of the group's poetry. This can be done quickly and inexpensively with a copy machine and a stapler. Copies can be distributed, even sold, to friends and relatives.
As you explore possible sources of publication--sampling books and magazines at the library, purchasing or subscribing to favorites--you'll sense where your poems might fit into the poetic universe.
If you find a magazine or website that often features poems you like, consider submitting some of your own. The websites listed above are only a few of the many that publish new writers. If you're more interested in traditional print media, check out the Poet's Market or International Directory of Little Magazines and Small Presses, both of which should be available at your local library.
Despite all this openness and opportunity, however, the publication process is often a process of selection. Editors frequently receive more submissions than they can print. All publishing poets learn to deal with rejection slips, to focus on the occasional acceptance and the sense of satisfaction that brings.
To increase the chances of acceptance, be selective in what you send out. Send your best work, poems that readers have enjoyed, poems that have been revised and edited. Submit them to your favorite magazines and websites.
Refrigerator door, blog, or elite literary journal--whatever your means of publication, it's worth taking that final step toward publication as a way of sharing your best with the world.
Once you've composed, shared, and revised a poem, you may want to take it public. Besides using the blog on this site, many other options are available.