Decide whether your poem will be traditional or modern. Traditional poetry can be challenging, because it's often rhymed and metered, such as a sonnet or villanelle. The structure of traditional forms makes it harder to express yourself. But when done well, a traditional poem has not just meaning, but subtle rhythms and music, almost like that of a song. Writing a traditional, metered form of poetry can be deeply satisfying. If you choose to write in the modern style, you have more freedom of expression, since most modern poems follow no absolute rules as to form. As a result, poetry of this kind is often wildly imaginative and fresh, juxtaposing unexpected or even dissonant images and concepts.
Choose the poet about whom you want to write your poem. There are a world of candidates, ranging from the famous and ancient, like the Greek poet Homer, to the recent and obscure, like that strange guy who read at your neighborhood coffeehouse Friday night. Again, no rules --- do you want to praise a genius like Alexander Pope or take a leaf from his book and write satire about a poet who makes no sense to you at all? It's your poem --- follow your own star.
Decide what you want to say. Did Lewis Carroll's "Jabberwocky" make you laugh --- and inspire you to try your hand at nonsense rhymes? Perhaps you admire seldom-remembered poets like Clement Clarke Moore, who gave the world "The Night Before Christmas," or Emma Lazarus, who wrote the world-famous lines, now inscribed on the base of the Statue of Liberty: "Give me your tired, your poor/Your huddled masses yearning to breathe free/The wretched refuse of your teeming shore/Send these, the homeless, tempest-tost, to me."
Start by writing the thoughts that come into your mind. Don't try to rush or force them. Some of the best ideas come at odd moments. Keep a pen and paper handy, so you can jot them down as they come to you. Above all, enjoy yourself. And don't throw away your poem once the assignment is over. It's proof that you can do it.