Submitting poems to a contest or a literary magazine goes beyond searching the Web, finding a likely contest, attaching a file and sending it on its merry way. To optimize the chances of your poetry being accepted, you need to do a lot more work.
Read some of the writing in the last issue of the magazine or contest.
Online or in print, many literary magazines feature work from the last issue on their website. This gives readers -- and writers -- an idea of the character of the publication. If you aren't submitting to a literary magazine, you should definitely read the winning poems from the last contest.
Always, always read the submission guidelines.
If you have not read the submission guidelines, it will likely be obvious to whoever has to read your submission. It might color their impression of you and your writing. Not following the submission guidelines sends the message, "My writing is too brilliant for me to bother following your guidelines." It goes beyond simple preparedness. It's a matter of respect and professionalism. Yours is one of many submissions the judges will read -- one among many others who did follow the contest guidelines. In some cases, failure to follow the guidelines will automatically eliminate you from the contest.
Reading the guidelines may also save you from sending an irrelevant or off-topic poem to the contest or magazine. Many specify what type, tone and/or topic of poetry they are looking for. Some contests want poems about war, some tell the poet to leave their politics out of it, some prefer rhyming poetry, others ban rhyming and some request poems based on personal experiences. Those are just a few examples of the different kinds of contests you can enter.
Some guidelines, however, are not spelled out directly.
This is where reading previous issues of the magazine or contest can help. These unwritten guidelines are the character of the contest or magazine: the tone, mood, type, length, style, etc. of the poems that they prefer to publish.
Read the previous entries in the contest or the current issue of the magazine. Is your poetry a good fit? It might be great poetry, but your poems on dark, gruesome topics won't fit with a contest asking for inspirational poetry or a publication whose poems look on the bright side of life. It will be clear to the judge that you haven't done your research, and your poem will likely be rejected out of hand.
Which poems should you submit?
For example, say you have five poems lined up to submit to a contest. They might be your best five -- but are they the best five for that contest? Based on what you've read, is there another poem that might be a better fit for this publication?
Sometimes it's worth pulling out a poem you don't like as much and revising it for submission if it fits the personality of a magazine or contest. Chances are you will end up liking the poem a lot more and appreciating the work you put into it, even if it is not accepted for publication. That said...
Don't write for the contest.
This is not to say that writers should tailor their poetry to the contest. On the contrary, sometimes it is better to search for a contest that fits the character of your writing. Also, while you might have your favorite poems, those aren't the only poems in your pocket -- and they shouldn't be the only poems you submit to contests. Every poet has a diverse mix of poems to draw from. Some contests won't be for you, and you absolutely shouldn't have to change your style to suit a particular contest. Keep writing, do your research, and you'll find a contest or literary magazine that might accept your work.