Be free, but set your rhythm. There is no particular structure to a satire poem. It can be written in any style you see fit, including free verse. It is, however, advised that you develop a rhyme scheme for your poem, as it adds rhythm and humor, masking the insult contained.
Get your inspiration from anywhere. When making a satire poem, the range of topics is endless. If you are choosing to criticize somebody or something, be passionate about what you are writing about, to get your point across effectively. You might choose to make fun of a husband-wife relationship, as satirical poet Sam Walter Foss does in "The Ideal Husband to his Wife."
Think about what you disapprove of or do not agree with in regards to this person or group. List the aspects of your subject that you think deserve satire. These aspects may include certain beliefs, opinions, lifestyle choices that the person or group might possess. If you are writing about male models, for example, you could draw attention to the fact that they wax their chests.
Try not to make the insult and criticism too obvious. Good, effective satiric poetry should be filled with your unique humor and wit and use intelligent words and phrases to create a subtle and funny message. Use your subject and aspects you wish to ridicule to develop the stanzas and overall structure of your poem.