Collect and read alliterative poems. Read them aloud to get a feel for the flow of repeating sounds.
Choose a subject or theme for your poem. For example, you may write your poem about a favorite tree you liked to climb as a child.
Write a list of words related to your poem's theme or words that remind you of or describe your poem's theme. Some but not all the words might start with the same letter as your topic. For the tree example, you might write: tall, branches, climbing, leaves, trunk, towering, lovely, shade and so on.
Organize the words you used into groups based on the letter sounds with which the words begin. In the tree example, you'd put tall, towering and trunk in one group, lovely and leaves in another and shade, branches and climbing would remain on their own.
Write more related words in each group, creating a list of words that start with the same sound. Combine your groups of similar-sounding words into sentences. Create sets of related sentences from the sentences with similar sounds. Try to make your poem's lines narrative, descriptive or related in some loose fashion; for the tree example, you'd still want the lines to tell a story about or set a scene at that childhood tree.
Read the poem you just wrote aloud and make sure all the sounds flow well together.