Publishing poems should not cost you anything. Reputable publishers pay you, not the other way around! Generally, you create a chapbook which you submit to various publishing companies. Try college presses or small, independent presses. You might also consider seeking out writing groups in your area to see where people are publishing their works.
You can also submit individual pieces (or a small number of selection) to various literary magazines. If there is an artsy area or college in your town, head to the bookstore and check out the magazine racks. Browsing or purchasing a couple of different types of magazines will help you to understand what sort of poetry makes it into their magazine.
Poetry jams were all the rage a few years back. Personally, I find them really rather annoying, but that's just my taste. However, some people might enjoy that environment. As they are usually held in bars or clubs, you might be able speak to some of the performers (poets) to learn more about local options for poets.
Try the library for resource books like "the Writer's Market" which is a giant guide of various magazines and publishing houses which is updated yearly. You can buy it, but it's a thick hardcover and it costs some doughsky.
just some thoughts...