Decide what story you want to tell in your poem. It can be silly, romantic, informative, descriptive or any type of story you want to write.
Brainstorm words that would fit into your poem. If you want to write poem for a friend, write all of the characteristics of your friend that you can.
Write a sentence that ends in one of the words you have listed about your subject. Determine the mood of the poem by the sentence you construct. A silly poem about your barber will be worded differently than a romantic poem about the new guy in accounting.
Search a rhyming dictionary the word at the end of the first line of your poem. At rhymezone.com, enter the word into the search box to get a list of words that rhyme with your word. The list is divided into number of syllables. If you can't find a word that matches your poem, click on near matches. These are words that sound like a close enough rhyme. A rhyming dictionary is formatted a little differently. You look up the last sound of the word you want to rhyme. For example, if you wanted to look up share, you would look under "A" for the "air" sound.
Choose the word that rhymes with the word you have at the end of your first sentence and which also will move your story along. Make a sentence with that word at the end of the sentence.
Read the two lines out loud to see if it sounds good, makes sense and conveys the message you want to convey. If it does, repeat it for the next two lines until your story is completely told.