Find Your Trigger
When you begin a poem, start with a clear, concrete situation, image or idea. Many poets are inspired by a "trigger" they have encountered in real life. Triggers can be anything from conversations, conflicts, memories, sights, sounds, phrases and so on. These are experiences that evoke feelings and/or questions, and are often sensual in nature, meaning they play upon one or more of the five senses.
Whatever gets you writing your poem might have nothing to do with what unravels at its end. More often than not, poets aren't truly aware of why any given trigger inspired them to set pen to paper. The touched nerve or "meaning" behind a trigger has to be discovered through the writing of the poem. As such, don't worry about expressing meaning or specific feelings in your first drafts.
Trust Your Voice
What differentiates one poet's work from another's often has more to do with voice than subject matter. Readers want to "hear" who you really are. That means attempts to sound hyper-intelligent by using archaic, latinate, or polysyllabic words will distance you from your reader and cause your voice to seem synthetic. Poetry is not about stringing together ornate words that have no meaning, nor is it about clouding your feelings with riddles. You cannot make a connection with your readers if they can't understand what you're saying.
Because poets are challenged to communicate what they think and feel with as much economy and concision as possible, it's vital that you choose your words wisely. In fact, the simpler, the better. Try for a natural, relaxed, conversational tone in plain, everyday language -- language you actually use. Place an emphasis on nouns and verbs; use adverbs sparingly and adjectives even more sparingly.
Poetry is an art form that makes use of metaphors, allusions and more. Whenever possible, instead of explicitly stating what it is you're trying to say, select a precise image or analogy that vividly conveys that same idea. If you've chosen your poetic devices wisely, you can trust your reader to understand what you're trying to say.
Focus on moving your reader from your initial idea to some new realization. Poets use the term "volta" or "turn" to describe the place within a poem where whatever the reader -- and, sometimes, the writer -- thought the poem was about changes, and a new idea, confession or conveyance of feeling is revealed. Allow your thoughts to link and travel organically. Write and write until you have happened upon a surprise -- that turn in your understanding, that insight into what made your initial idea so intriguing.
Revision is where much of a poet's work is done. Technically, to revise is to see things in a new way. That means looking at your work with fresh eyes, as objectively as possible. Ask: Is it honest? Is there more that wants to be said? Is any part confusing? Is it predictable? Could the language be more interesting, precise, or surprising? Does it allow for strangeness? Should I change the voice, the speaker, the point of view? What needs to be cut?
Make changes according to your answers.