Making a living off of poetry is almost non-existant. There is little money to be made from competitions and publications. The most it can do is enhance a reputation. If you are an author for example and you're looking for an agent then you may be viewed as a more promising candidate were you to be published in several magazines. There are several poetry magazines and ezines online that usually accept submissions. There are also several poetry contests, but beware there are a lot of poetry scams out there that just want your money.
Sites like lulu.com and others offer chapter books. You can try making a living off selling your books online but it's very difficult and most often, unprofitable. It would make a nice gift for your family and friends, as long as you don't go all suicidal in it. Self publication is also good for presentation if you want to present your book to an editor.
Try fastweb.com, they have thousands of scholarships. Maybe not poetry, but they have several essay contests. There's a lot of scams out there and rarely do poetry contests and offers make money without there being a catch or statistical gamble that ensures the company makes a great deal of money off the odds.