The issue of vanity press arises in various guises. Johnathon Clifford has devoted himself to the issue - see his WWW page
Self-publishing is an old and honorable venture. Many famous poets started in this way. In some newspapers you'll see ads from certain presses asking for manuscripts. Having something published in this way costs more, and though the presses sometimes claim that they'll distribute and advertise for you, bookshops steer well clear of such presses. Mentioning that you've been published by them will tarnish your reputation. Some of these 'joint venture', or 'subsidy' publishers have appeared in court because of their misleading claims. That said, some small presses who require up-front money from authors have a good reputation.
Another ploy used by publishers is to solicit poems for an anthology and accept most (or maybe all) the poems sent in. The resulting huge anthology is bought by the proud poet and the publisher makes a worthwhile profit.
In the small press world there's a disguised form of paying to be published. Some magazines will only accept contributions from subscribers. One can understand why they do this, but it does rather muddy the waters. There are also competitions (in the USA especially) where the winner has a book published. In the UK the Poetry Business runs such a competition and publish some excellent books as a result, but there's a hefty entry fee (18 pounds).
So beware. Decide why you want to be published and pick the most appropriate method. Remember that poetry books don't sell (even well known poets have trouble shifting 300 copies), so if you want to be read perhaps you should submit to magazines or put your material on the WWW. If you want a "real" book with an ISBN merely for posterity's sake or to distribute to friends, you don't really need the expense of a publisher.